triangles. Answer (e) q = Answer (b) q = (c) q = (d) q = opp 9.4 adj 7.61 angle (f) q = triangles.

Transcription

1 1 Use trig to solve the following problems. (a) Find q if tan q = (b) Find q if sin q = (c) Find q if cos q = (d) Find q if tan q = (e) Find q if sin q = (f) Find q if cos q = Solve for all sides and all angles for the following right triangles. (a) q = (b) q = (c) q = (d) q = (e) q = (f) q = opp 9.4 adj 7.61 angle Use trig to solve the following problems. (a) Find the tan (b) Find the sin (c) Find the cos (d) Find the tan 58 0 (e) Find the sin 40 0 (f) Find the cos Solve for all sides and all angles for the following right triangles. (a) 0.53 (b) 1.00 (c) 1.00 (d) 1.6 (c) 0.64 (f) 0.33 hyp 9.65 adj 5.1 angle opp 5.1 angle Solve for all sides and all angles for the following right triangles. 6 Solve for all sides and all angles for the following right triangles. hypothesis 4.7 opp 2.5 angle 32 0 Missing side 9.62 adj 7.0 side angle 54 0 opp 7.0 side 36 0

2 7 Solve for all sides and all angles for the following right triangles. 10 Solve for all sides and all angles for the following right triangles. 8 hypothesis 4.7 opp 2.5 angle 32 0 Solve for all sides and all angles for the following right triangles. 11 Missing side 9.62 adj 7.0 side angle 54 0 opp 7.0 side 36 0 The French bomber Mirage IV can reach a speed of more than 2.3 x 10 3 km/h. Suppose this plane accelerates at a rate that allows it to increase its speed from 6.0 x 10 2 km/h to 2.3 x 10 3 km/h in a time interval of 120 s. If this acceleration is upward and at an angle of 35 0 with the horizontal, find the acceleration's horizontal and vertical components. 9 opp 9.4 adj 7.61 angle 51 0 Solve for all sides and all angles for the following right triangles m/s 2 horizontally 2.2 m/s 2 vertically A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of 60 0 with the floor. A force of 75 N is exerted on the rope. What is the component of the force parallel to the floor? 37.5 N 13 A hiker walks 14.7 km at an angle of 35 0 south of east. Find the east-west and north-south components of this walk. hyp 9.65 adj 5.1 angle opp 5.1 angle km, south 12.0 km, east Find the vertical and horizontal components of an acceleration of 50 m/s 2 that is directed 50 0 above the horizontal m/s 2. vert 32.2 m/s 2. horiz

3 15 Iguanas, which are found in Costa Rica, have been observed to run as fast as 10.0 m/s. Suppose an iguana runs in a straight line at this speed for 5.00 s. The direction of motion makes an angle of to the east of the northward direction. Find the value of the iguana's northward displacement. 19 In Virginia during 1994 Elmer Trett reached a speed of 372 km/h on his motorcycle. Suppose Trett rode northeast at this speed for 8.0 s. (a) If the angle between east and the direction of Trett's ride was , what was Trett's displacement east? (b) What was his displacement north? m The landing speed of the space shuttle Columbia is 347 km/h. If the shuttle is landing at an angle of with respect to the horizontal, what are the horizontal and vertical components of its velocity? m east 716 m north Identify a convenient coordinate system for a person climbing a ladder at an angle of 70 0 to the ground km/h Horizontal 89.8 km/h Vertical A South African sharp-nosed frog set a record for a triple jump by traveling a distance of 10.3 m. Suppose the frog starts from the origin of a coordinate system and lands at a point whose coordinate on the y-axis is equal to m. (a) What angle does the vector of displacement make with the negative y-axis? (b) Calculate the x-axis coordinate of the frog. 21 x-axis: horizontal along the ground y-axis: up and down A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 35 m/s. At the same time, it has a horizontal velocity of 55 m/s. (a) At what speed does the vehicle move along its descent path? (b) At what angle with the vertical is this path? (a) 65.2 m/s; (b) m The longest delivery flight ever made by a twin-engine commercial jet took place in The plane covered a total distance of 14,890 km from Seattle, Washington, to Nairobi, Kenya, in 18 h, 29 min. (a) Assuming that the plane flew in a straight line between the two cities, find the magnitude of the average velocity of the plane. (b) Find the eastward and southward components of the average velocity if the direction of the plane's flight was at an angle of south of east A weather station releases a weather balloon. The balloon's buoyancy accelerates it straight up at 15 m/s 2. At the same time, a wind accelerates it horizontally at 6.5 m/s 2. What is the magnitude and direction (with reference to the horizontal) of the resultant acceleration? 16 m/s (up from horizontal) A spacecraft landing on the moon has a downward displacement of 650 m on a flight path that makes an angle of 58 0 from the vertical. (a) What is the spacecraft's vertical displacement? (b) What is the spacecraft's horizontal displacement? km/h km/h east km/h south (a) 550 m horizontal (b) 330 m vertical

4 24 A rocket is aimed at a neighboring city with a displacement of 1120 m/s. The city is located on a bearing of (a) What are the directions and magnitudes of its North-South component? (b) What is the directions and magnitude of its East-West component? 29 The man pulls with a force of 25.0 N at an angle of to the horizontal. (a) Find the x component of this force. (b) Find the y component of this force. (a) South 500 m (b) East 1000 m (a) 23.8 N (b) 7.73 N 25 An airplane flies on a bearing of at 525 km. What are the components of the plane's displacement? 30 A girl delivering newspapers covers her route by traveling three blocks west, four blocks north, and then six blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels? 450 m South 270 m East 26 How fast must a truck travel to stay beneath an airplane that has moved 105 km at an angle of 25 0 from the ground? (a) 5 blocks at 500 north of east (b) 13 blocks 27 94,000 km What are the horizontal and vertical components of a cat s displacement when it is climbing 5 m directly up a tree? 31 Cheetahs can run with a speed as great as 30.0 m/s (more than 100 km/h). In the course of a chase, cheetahs can also change direction very quickly. Suppose a cheetah runs straight north at maximum speed for 5.00 s, quickly stops, and runs 3.00 x 10 2 m west. Find the magnitude of the cheetah's resultant displacement. 0 m horizontal 5 m vertical x 10 2 m 28 A submarine dives m at an angle of below the horizontal. What are the horizontal and vertical components of the submarine s displacement? 32 While flying due east at 120 km/h, an airplane is also carried northward at 45 km/h by the wind blowing due north. What is the plane's resultant velocity? 108 m, m 130 km/h 21 0 north of east Bearing Kyle is flying a plane due north at 225 km/h as a wind carries it due east at 55 km/h. Find the magnitude and direction of the plane's resultant velocity analytically. 230 km/h,

5 34 Sue and Jenny kick a soccer ball at exactly the same time. Sue's foot exerts a force of 66 N north. Jenny's foot exerts a force of 88 N east. What is the magnitude and direction of the resultant force on the ball? 38 An ostrich cannot fly, but it makes up for it by being able to run fast. Ostriches have been observed to reach speeds of up to 20.0 m/s. Suppose an ostrich runs east at 20.0 m/s during a time interval. It then turns northward and runs at the same speed for the same amount of time. Calculate t if the magnitude of the ostrich's resultant displacement from its starting point is 226 m. 1.1 x 10 2 N 37 0 North of east 53 0 East of north Bearing s 35 A 110-N force and a 55-N force both act on an object point P. The 110-N force acts at The 55-N force act at 0 0. What is the magnitude and direction of the resultant force? 122 N An emperor penguin is the best diver among birds: the record dive is 483 m. Suppose a penguin dives vertically to a depth of 483 m and then swims horizontally a distance of 225 m. (a) What angle would the vector of the resultant displacement make with the vertical direction? (b) What is the magnitude of the penguin's resultant displacement? 36 The pronghorn antelope, found in North America, is the best long distance runner among mammals. It has been observed to travel at an average speed of more than 55 km/h over a distance of 6.0 km. Suppose the antelope runs a distance of 6.0 km in the following manner: it travels 2.0 km in one direction, then turns 90 0 and runs another 4.0 km. Calculate the magnitude of the resultant displacement and the angle the resultant vector makes with the vector for the initial displacement m Woodcocks are the slowest flyers among birds: their average speed during courtship displays can be as slow as 8.00 km/h. Suppose a woodcock flies east for 15.0 min. It then turns and flies for 22.0 min in the northern direction. Calculate the magnitude of the resultant displacement and the angle between the resultant displacement and the woodcock's initial displacement. 4.5 km above the horizontal km A killer whale can swim as fast as 15.0 m/s. Suppose a killer whale swims in one direction at this speed for 8.0 s, makes a 90 0 turn, and continues swimming in the new direction with the same speed as before. After a certain time interval, the magnitude of the resultant displacement is m. Determine the amount of time the whale swims after changing direction. 8.9 s 41 In 1926, Gertrude Ederle of the United States became the first woman to swim across the English Channel. She covered a distance of about 33 km. Suppose Ederle swam 33.0 km from Dover, England, to Calais, France, and then made a 90 0 turn and traveled westward for 11.0 km. (a) Assuming that the first leg of Ederle's swim was in the southern direction, what was the magnitude of her resultant displacement? (b) What was the angle between Ederle's resultant displacement and her initial displacement? 34.8 km west of south

6 42 Tammy leaves the office, drives 26 km due north, then turns onto a second highway and continues in a direction of north of east for 62 km. What is her total displacement from the office? 78.3 km 47 0 N of E 43 0 bearing 46 In 1976, a U.S. Air Force jet reached the highest recorded speed for any airplane: 3.53 x 10 3 km/h. Suppose you observe a plane ascending at this speed. For 20.0 s, it flies at an angle of above the horizontal, then for another 10.0 s its angle of ascent is increased by another (a) Calculate the total gain in altitude during this 30.0 s interval (b) Calculate the total horizontal displacement of the airplane. 43 Two 15-m/s 2 accelerations act concurrently on point P. (a) Find the magnitude of their resultant when the angle between them is (b) Find the magnitude of their resultant when the angle between them is (c) Find the magnitude of their resultant when the angle between them is (d) Find the magnitude of their resultant when the angle between them is (e) Find the magnitude of their resultant when the angle between them is x 10 4 m 2.59 x 10 4 m Magnor Mydland, of Norway, constructed a motorcycle with a wheel base of about 12 cm. The tiny vehicle could be ridden at a maximum speed of 11.6 km/h. Suppose this motorcycle travels in the directions shown in the figure below. If the motorcycle travels at maximum speed, how much time is needed for it to reach a net displacement of 2.00 x 10 2 m to the right? 44 (a) 30 m/s 2 (b) 29 m/s 2 (c) 21 m/s 2 (d) 15 m/s 2 (e) 0 m/s 2 The record for the longest nonstop closed-circuit flight by a model airplane was set in Italy in The plane flew a total distance of 1239 km. Assume that at some point the plane traveled 1.23 x 10 3 m to the east, then 1.25 x 10 3 m to the north, and finally 1.00 x 10 3 m to the southeast. Calculate the magnitude of the displacement for this portion of the flight s The fastest propeller-driven aircraft is the Russian TU-95/142, which can reach a maximum speed of 925 km/h. For this speed, calculate the net displacement for the plane if it travels east for 1.50 h, then turns to the northwest and travels in that direction for 2.00 h. 1.3 x 10 6 m east of north m Over the course of about six weeks in 1992, Akira Matsushima, from Japan, rode a unicycle more than 3000 m across the United States. Suppose Matsushima is riding through a city. If he travels m east on one street, then turns counterclockwise through a angle and proceeds m northwest along a diagonal street, what is his net displacement? 49 In 1952, the ocean liner United States crossed the Atlantic Ocean in less than four days, setting the world record for commercial ocean-going vessels. The average speed for the trip was about 66.0 km/h. Suppose the liner moves in a straight line eastward at this speed for 2.50 h. Then, due to a strong local current, the ship's course begins to deviate northward by , and the liner follows the new course at the same speed for another 1.50 h. Find the net displacement for the 4.0 h period x 10 5 m north of east 78.8 bearing m north of east

7 50 Find the resultant displacement of a fox searching for mice in a prairie. First the fox heads 55 0 north of west for 10.0 m; then it turns and heads west for 5.0 m. 53 An archaeologist climbs the Great Pyramid in Giza, Egypt. If the pyramid s height is 136 m and its width is 2.30 x 10 2 m, what is the magnitude and the direction of the archaeologist s displacement while climbing from the bottom of the pyramid to the top? 13.5 m 37 0 north of west bearing Solve Graphically 51 The largest variety of grasshopper in the world is found in Malaysia. These grasshoppers can measure almost a foot (0.305 m) in length and can jump 4.5 m. Suppose one of these grasshoppers starts at the origin of a coordinate system and makes exactly eight jumps in a straight line that makes an angle of 35 0 with the positive x-axis. Find the grasshopper's displacements along the x- and y-axes. Assume y is positive m While following the directions on a treasure map, a pirate walks 45.0 m north, then turns and walks 7.5 m east. What single straight line displacement could the pirate have taken to reach the treasure? m x direction 21 m y direction The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction north of west with a speed of 41.0 km/h. Exactly three hours later, the course of the hurricane shifts due north, and its speed slows to 25.0 km/h, as shown in the figure below. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island? 55 Solve Graphically 47 m east of north Emily passes a soccer ball 6.0 m directly across the field to Kara, who then kicks the ball 14.5 m directly down the field to Louisa. What is the magnitude of the ball s total displacement as it travels between Emily and Louisa? Solve Graphically 15.7 m 56 A novice pilot sets a plane s controls, thinking the plane will fly at 250 km to the north. If the wind can blow the plane off course by 75 km toward the southeast, what is the plane s resultant displacement? 157 km 210 km 75 0 bearing 15 0

8 57 Find the magnitude and direction of the resultant of a 5 N force that acts at an angle of 37 0 clockwise from the +X axis, a 3 N force that acts at an angle of clockwise from the +X axis, and a 7 N force that acts at an angle of clockwise from the +X axis. 62 Find the magnitude and direction of the resultant of a 60 N force that acts at an angle of 45 0 clockwise from the +Y axis, a 20 N force that acts at an angle of 90 0 from the +Y axis, and a 40 N force that acts at an angle of clockwise from the +Y axis. 4.4 N clockwise from the +X axis. 68 N at 24 0 clockwise from the +Y axis 58 Kangaroos can easily jump as far 8.0 m. A kangaroo makes five such jumps westward and then seven such jumps northward. (a) What angle?, would the resultant displacement vector make with the northern displacement vector? (b) What is the magnitude of the total displacement? 63 A person walks the path shown in the figure below. The total trip consists of four straight-line paths. At the end of the walk, what is the person s resultant displacement measured from the starting point? 36 0 west of the north Bearing m displacement vector 59 Find the magnitude and direction of the resultant of a 5 m displacement that acts at an angle of 37 0 clockwise from the +X axis, a 3 m displacement that acts at an angle of clockwise from the +X axis, and a 7 m displacement that acts at an angle of clockwise from the +X axis x 10 2 m South of West bearing m clockwise from the +X axis. The water used in many fountains is recycled. For instance, a single water particle in a fountain travels through an 85 m system and then returns to the same point. What is the displacement of a water particle during one cycle? 64 Three superstrong teenagers push a heavy crate across the floor. Dion pushes with a displacement of 18.5 m at 0 0. Shirley pushes with a displacement of 16.5 m at 30 0, while Joan pushes with a displacement of 19.5 m at What is the resultant displacement on the crate? Zero 43.4 m west of north Bearing Joanne pulls on a trunk with a 12-N force. Bev pulls at right angles to Joanne. How hard must Bev pull to make the resultant force on the trunk 13 N? 65 Find the magnitude and direction of the resultant of a 60 m displacement that acts at an angle of 45 0 clockwise from the +Y axis, a 20 m displacement that acts at an angle of 90 0 from the +Y axis, and a 40 m displacement that acts at an angle of clockwise from the +Y axis. 5 N 68 m 240 clockwise from the +Y axis

9 66 An airplane flies on a bearing of It travels 525 km. in 3 hours. What are the components of the plane's average velocity? 70 A race car traveling 45 m/s 55 0 North of West is slowed uniformly at the rate of -1.5 m/s 2 for ten seconds. (a) What is its final velocity of the race car in m/s? (b) What are the components of the final velocity? (c) What are the components of the initial velocity? (d) What is the diplacement of the car? (e) What are the components of the car s displacement? (f) What are the components of the car s acceleration? A racing car s velocity is increased uniformly from 44 m/s, to 66 m/s, at a bearing of over an 11 second period. (a) What is the acceleration of the car? (b) What is the displacement of the car? (b) What are the components of the car s acceleration? (c) What are the final componets of the car s displacement? (a) 2.0 m/s 2 (b) 605 m (c) Vert Horz (d) m Vert m H A train-moving 55 0 east of south at a velocity of 15 m/s is accelerated uniformly to 17 m/s west over a 12-s period. (a) Draw a vector diagram of the train s initial velocity? (b) What is the acceleration of the train? (c) What is the direction of the train? (d) What is the displacement of the train? (e) What are the components of the train s acceleration? (c) What are the final components of the train s displacement? (Hard) m/s, east The fastest speed ever achieved by a vessel on the water is 555 km/h, which was achieved in 1977 off the coast of Australia. Suppose the vessel undergoes an average acceleration of 1.8 m/s 2 at a bearing of The vessel accelerates for 1.0 minute from rest. (a) What is its speed after that minute in km/hr? (b) What is its speed after that minute in m/s? (c) What are the components of the final velocity? (d) What are the components of the initial velocity? (e) What is the diplacement of the car? (f) What are the components of the car s displacement? (g) What are the components of the car s acceleration? (a) 3.89 x 10 2 km/hr (b) 108 m/s South African frogs are capable of jumping as far as 10.0 m in one hop. Suppose one of these frogs makes exactly 15 of these jumps in a time interval of 60.0 s at a bearing of (a) What is the frog's average speed? (b) What are the components of the frog s average speed? 69 (a).166 m/s 2, (b) (c) (d) A car is uniformly accelerated at the rate of +1.2 m/s 2 for 12 s at a bearing of The original velocity of the car is +8.0 m/s. (a) What is its final velocity? (b) What are the components of the final velocity? (c) What are the components of the initial velocity? (d) What is the diplacement of the car? (e) What are the components of the car s displacement? (f) What are the components of the car s acceleration? If the frog lands with a speed equal to its average speed and comes to a full stop 0.25 s later, (b) What is the magnitude of its average deceleration? (c) What are the components of the frog s displacement? (d) What are the components of the frog s acceleration? (a) 2.50 m/s (b) -10 m/s m/s

10 73 74 The first permanent public railway was built by George Stephenson and opened in Cleveland, Ohio, in The average speed of the trains was 24.0 km/h. Suppose a train moving at this speed begins decelerating by 0.20 m/s 2 in a direction of 22 0 East of North until it reaches a speed of 8.0 km/h. (a) Find the time it takes the train to decelerate. (b) What are the components of the final velocity? (c) What are the components of the initial velocity? (d) What is the diplacement of the train? (e) What are the components of the train s displacement? (f) What are the components of the train s acceleration? 22 s Mary Rife, of Texas, set a women's world speed record for sailing. In 1977, her vessel, Proud Mary, reached a speed of 3.17 x 10 2 km/h at a bearing of Suppose it takes 8.0 s for the boat to decelerate from its top speed to a speed of 2.00 x 10 2 km/h. (a) What is the magnitude of the deceleration? (b) What distance is traveled as Proud Mary slows down? (c) What are the components of the vessel Proud Mary s final velocity? (d) What are the components of the vessel Proud Mary s initial velocity? (e) What is the diplacement of the vessel Proud Mary? (f) What are the components of the vessel Proud Mary? displacement? (g) What are the components of the vessel Proud Mary? acceleration? An automobile, which set the world record for acceleration, increased speed from rest to 96.0 km/h in 3.07 s at a bearing of (a) What distance was traveled by the time the final speed was achieved? (b) What are the components of the displacement? 41.0 m A car moving 13 0 West of North along a straight, level road increases its velocity uniformly from +16 m/s to +32 m/s in 10.0 s. (a) What is the car's acceleration? (b) What is its average velocity? (c) How far did it move while accelerating? (b) What are the components of the final velocity? (c) What are the components of the initial velocity? (d) What is the diplacement of the car? (e) What are the components of the car s displacement? (f) What are the components of the car s acceleration? (a) +1.6 m/s 2 (b) +24 m/s (c) 240m An airplane starts from rest and undergoes a uniform acceleration of +3.0 m/s 2 for 30.0 s at a bearing of before leaving the ground. (a) What is this displacement during the 30.0 s? (b) What are the components of this displacement? (a) (b) 8.3 x 10 2 m 1350 m 75 In 1990, Dave Campos of the United States rode a special motorcycle called Easyrider at an average speed of 518 km/h. Suppose that at some point he steadily decreases his speed from percent to 60.0 percent of his average speed during an interval of 2.00 min at a bearing of (a) What is the distance traveled during that time interval? (b) What are the components of the final velocity? (c) What are the components of the initial velocity? (d) What is the diplacement of the motorcycle? (e) What are the components of the motorcycle s displacement? (f) What are the components of the motorcycle s acceleration? 79 The Tokyo Express is uniformly accelerates from rest at +1.0 m/s 2 for 1.0 min. in a direction of 20 0 North of West. (a) How far does it travel during this time? (b) What are the components of the displacement during this time interval? (c) What are the components of its acceleration? 1800 m 13.8 km

11 80 A car starting from rest is accelerated at the constant rate of 3.0 m/s 2 in a direction of 27 0 South of West? (a) What is its speed at the end of 8.0 s? (b) How far did it travel during the first 8.0 s? (c) What are the components of the final velocity? (d) What are the components of the initial velocity? 84 The lightest car in the world was built in London and weighed less than 10 kg. Its maximum speed was 5.0 km/h. Suppose the driver of this vehicle applies the brakes while the car is moving at its maximum speed and at a bearing of The car stops after traveling 16.0 m. (a) Calculate the magnitude of the deceleration. (b) What are the components of the car s deceleration? (a) 24 m (b) 96 m m/s 2 81 The world's fastest warship belongs to the United States Navy. This vessel, which floats on a cushion of air, can move as fast as 1.7 x 10 2 km/h. Suppose that during a training exercise the ship is moving at 20.0 m/s at a bearing of when it begins to accelerate. After 15.0 s of accelerating, a distance of m is traveled. (a) Calculate the value for the acceleration during the ship's displacement. (f) What are the components of the warship s acceleration? 85 The skid marks left by the decelerating jet-powered car The Spirit of America were 9.6 km long. The car decelerated at the rate of 2.0 m/s 2 at a bearing of (a) What was the initial veloicty of the car? (b) What are the componets of the car s initial velocity? 7.2 x 10 2 km/h m/s m/s 2 The highest speed to be achieved by a standard non-racing sports car is 3.50 x 10 2 km/h. Assume the car accelerates at 4.00 m/s 2 at a bearing of (a) How long would this car take to reach its maximum speed if it is initially at rest? (b) What distance would the car travel during this time? (c) What are the components of the car s displacement? (d) What are the components of the car s acceleration? 86 With a cruising speed of 2.30 x 10 3 km/h, the French supersonic passenger jet Concorde is the fastest commercial airplane. Suppose the landing speed is 20.0 percent of the cruising speed and lands on a runway alligned in a direction of 25 0 West of North? (a) Over what distance does the plane travel to a complete stop if its deceleration has a magnitude of 5.80 m/s 2? (b) What are the components of the displacement? (a) (b) 1.18 x 10 3 m A bullet leaves the muzzle of a rifle with a speed of 600 m/s, at an angle of 20 0 above the horizontal. The barrel of the rifle is 0.9 m long, (a) What is the acceleration of the bullet while in the barrel? (b) What is the horizontal acceleration of the bullet? (c) What is the vertical acceleration of the bullet? 87 The Boeing 747 can carry more than 560 passengers and has a maximum speed of about 9.70 x 10 2 km/h. After takeoff; the plane takes a certain time to reach its maximum speed. Suppose the plane has a constant acceleration of 4.80 m/s on a bearing of 355 0? (a) What distance does the plane travel between the moment its speed is 50.0 percent of maximum and the moment its maximum speed is attained? (b) What are the components of the distance the plane traveled? 2 x 10 5 m/s km

12 88 A baby sitter pushing a stroller starts from rest and accelerates at a rate of m/s 2 in a direction of 53 0 south of west. (a) What is the velocity of the stroller after it has traveled 4.75 m? (b) What are the components of the stroller s velocity? 91 The graph shows the velocity of a motorcycle moving in a direction of 73 0 south of west. Assume that direction of the acceleration is along the same line as the velocity. (a) Determine the acceleration of the motorcycle at t = 1 second. (b) Determine the components of the acceleration at t = 1 second m/s 89 A plane starting at rest at the south end of a runway undergoes a constant acceleration of +1.6 m/s 2 for a distance of 1600 m in a direction of 23 0 West of South before takeoff. (a) What is the plane's velocity at takeoff (b) What are the component s of the plane s velocity? (c) What is the time required for takeoff? (a) 71.6 m/s (b) 44.7 s 90 A speedboat increases its velocity from 25 m/s to 35 m/s in a direction of 55 east of west for a distance of 250 m. (a) Find the magnitude of the boat's acceleration. (b) Find the components of the boat s acceleration. (c) Find the time it takes the boat to travel this distance. 92 The graph show the velocity of a train moving in a direction of 55 0 East of North. Assume that the train s acceleration is in the same direction as the velocity. (a) Find the acceleration of the object between the tenth and the fifteenth second of travel. (b) What are the components of the acceleration during between the tenth and the fifteenth second of travel. (a) 1 m/s 2 to the west (b) 8.3 s (a) 6 m/s 2 (b) 0 (c) -2 m/s 2 (d) -4 m/s 2

13 93 The graph show the velocity of a car moving in a direction of 55 0 East of South. Assume that the car s acceleration is in the same direction as the velocity. (a) What is the acceleration at t = 2.4 seconds? (b) What are the components of the acceleration at t = 2.4 seconds? 95 The graph show the velocity of a runner moving in a direction of 55 0 East of North. Assume that the runner s displacement is in the same direction as the velocity and acceleration. (a) Determine the distance traveled by the runner whose velocity-time graph is given in the figure to the left. Consider the full 8 second interval. (b) What are the components of the displacement during the full 8 second interval? 94 The graph show the velocity of a car moving in a direction of 25 0 East of South. Assume that the car s displacement is in the same direction as the velocity and acceleration. (a) How far an object moves during the first 4.5 seconds. (b) What are the components of the objects displacement during the first 4.5 seconds? m You head downstream on a river in a canoe. You can paddle at 5.0 km/h and the river is flowing at 2.0 km/h. How far downstream will you be in 30 minutes? 3.5 km; Refer to Problems and Solutions Manual. 97 You head downstream on a river in an outboard motorboat. The current is flowing at a rate of 1.50 m/s. After 30.0 min., you find that you have traveled 24.3 km. How long will it take you to travel back upstream to your original point of departure? 38.5 min.

14 98 Dave rows a boat across a river at 4.0 m/s. The river flows at 6.0 m/s and is 360 m across. (a) In what direction, relative to the shore, does Dave's boat go? (b) How long does it take Dave to cross the river? (c) How far downstream is Dave's landing point? (d) How long would it take Dave to cross the river if there were no current? 102 The resultant motion of a boat on a river is 20 km/h in a direction making an angle of 60 0 from the flow of the current. If the river is 1.5 km wide, how long does it take the boat to cross the river? h or 5.3 min. 99 (a) 340 relative to shore (b) 90s (c) 540 m (d) 90 s A motorboat travels at 8.5 m/s. It heads straight across a river 110 m wide. (a) If the water flows downstream at a rate of 3.8 m/s, what is the boat's resultant velocity? (b) How long does it take the boat to reach the opposite shore? 103 A man rows across a river at 4.0 mi/hr. The boat is always kept heading at right angles to the stream of water. The river is flowing at 6.0 mi/hr and is 0.20 mi across. (a) What direction and with what speed does the boat actually go relative to the shore. (b) How long does it take him to cross the river (c) How far downstream is his landing point from his starting point (d) How long would it take him to cross the river if there was no current? 100 (a) 9.3 m/s 24 0 (b) 13 s A boat heads directly across a river 41 m wide at 3.8 m/s. The current is flowing downstream at 2.2 m/s. (a) What is the resultant velocity of the boat? (b) How much time does it take the boat to cross the river? (c) How far downstream is the boat when it reaches the other side? 104 (a) 7.2 mph from current degrees from shore (b) 0.05 hr (c) 0.3 mi (d) 0.05 hr. A boat head northwest at 10 m/hr in a river that flows east at 3 m/hr. What is the magnitude and direction of the boat's velocity relative to the earth's surface (The resultant velocity of these two vectors does not form a right triangle). (a) 4.4 m/s 30 0 (b) 11 s (c) 24 m 8.2 m/hr 30 0 west of north. 101 A boat moving at 12 m/hr in still water moves perpendicular to a river current which is flowing at a speed of 4 m/hr. In what direction and with what speed should the boat head if it is to reach a point on the other side of the river directly opposite its starting point? 105 As a result of a combination of its own motion and that of a river current, a boat actually moves directly across the river at 8 km/hr. If the bow of the boat is pointed in a direction making an angle of 135 degrees from the flow of the current, what is the speed of the current? upstream m/hr a 8.0 km/h

15 106 Kym is in a boat traveling 3.8 m/s straight across a river 240 m wide. The river is flowing at 1.6 m/s. (a) What is Kym's resultant velocity? (b) How long does it take Kym to cross the river? (c) How far is Kym downstream when she reaches the other side? 110 A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s due north relative to the water. (a) What is the velocity of the boat as viewed by an observer on shore? (b) If the river is 325 m wide, how far downstream has the boat moved by the time it reaches the north shore? (a) 4.1 m/s, 67 0 (from bank); (b) 63 s; (c) m (a) 10.1 m/s at east of north (b) 48.8 m 107 Apply the Pythagorean theorem to find the magnitude of the resultant velocity vector for the following perpendicular velocities: (a) a fish swimming at 3.0 m/s 2 across a river that moves at 5.0 m/s 2 (b) a surfer traveling at 1.0 m/s 2 across a wave that is traveling at 6.0 m/s 111 A hunter wishes to cross a river that is 1.5 km wide and that flows with a speed of 5.0 km/h. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing? 0.12 h 108 (a) 5.8 m/s (b) 6.1ms Find the direction of the resultant velocities for each situation: (a) a fish swimming at 3.0 m/s 2 across a river that moves at 5.0 m/s 2 (b) a surfer traveling at 1.0 m/s 2 across a wave that is traveling at 6.0 m/s 112 A swimmer can swim in still water at a speed of 9.50 m/s. He intends to swim directly across a river that has a downstream current of 3.75 m/s. (a) What must the swimmer s heading be? (b) What is his velocity relative to the bank? (a) upstream from straight across (b) 8.72 m/s across the river 109 (a) 59 0 downriver from its intended path (b) from the direction the wave is traveling A boat heading north crosses a wide river with a velocity of km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the boat s velocity with respect to an observer on the shore. 113 A motorboat heads due east at 12 m/s across a river that flows toward the south at a speed of 3.5 m/s. (a) What is the resultant velocity relative to an observer on the shore? (b) If the river is 1360 m wide, how long does it take the boat to cross? km/h east of north with respect to the earth (a) 12 m/s at 16 0 south of cast (b) 113 m/s

16 114 A boat moves through a river at 7.5 m/s relative to the water, regardless of the boat s direction. If the water in the river is flowing at 1.5 m/s, how long does it take the boat to make a round trip consisting of a 250 m displacement downstream followed by a 250 m displacement upstream? 118 A spy runs from the front to the back of an aircraft carrier at a speed of 3.5 m/s. If the aircraft carrier is moving forward at 18.0 m/s, how fast does the spy appear to be running when viewed by an observer on a nearby stationary submarine? Show your work..70 sec, 14.5 m/s in the direction that the aircraft carrier is moving 115 A water spider maintains an average position on the surface of a stream by darting upstream (against the current), then drifting downstream (with the current) to its original position. The current in the stream is m/s relative to the shore, and the water spider darts upstream m (relative to a spot on shore) in s during the first part of its motion. Use upstream as the positive direction. (a) Determine both the velocity of the water spider relative to the water during its dash upstream and its velocity during its drift downstream. (b) How far upstream relative to the water does the water spider move during one cycle of this upstream and downstream motion? (c) What is the average velocity of the water spider relative to the water? (a) m/s, m/s (b) m (c) m/s A river flows at a bearing of 90. Mark, a riverboat pilot, heads the boat at 297 and is able to go straight across the river at 6.0 m/s. (a) What is the velocity of the current? (b) What is the velocity of the boat as seen from the river bank? (a) 11.8 m/s, 90 0 ; (b) 13.2 m/s, 0 0 Diane rows a boat at 8.0 m/s directly across a river that flows at 6.0 m/s. (a) What is the resultant speed of the boat? (b) If the stream is 240 m wide, how long will it take Diane to row across? (c) How far downstream will Diane be? The world's fastest current is in Slingsby Channel, Canada, where the speed of the water reaches 30.0 km/h. Suppose a motorboat crosses the channel perpendicular to the bank at a speed of 18.0 km/h relative to the bank. Find the velocity of the motorboat relative to the water km/h Turtles are fairly slow on the ground, but they are very good swimmers, as indicated by the reported speed of 9.0 m/s for the leatherback turtle. Suppose a leatherback turtle swims across a river at 9.0 m/s relative to the water. If the current in the river is 3.0 m/s and it moves at a right angle to the turtle's motion, how large is the turtle's displacement with respect to the river's bank after 1.0 min? 121 (a) 10 m/s, 53 0 (from bank); (b) 30 s; (c) 18 x 10 2 m A swimmer heads directly across a river, swimming at a maximum speed of 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide. (a) What is the speed of the river current? (b) What is the swimmer's speed relative to the shore? (c) In what direction should she head so as to arrive at the point directly opposite her starting point? (a).8 m/s (b) 1.78 m/s (c) x 10 2 m/s 18 0 to the side of vtw

17 122 An oceanliner is heading due north with a speed of 8.5 m/s relative to the water. A small sailboat is heading 45 0, east of north with a speed of 1.0 m/s relative to the water. Find the relative velocity (magnitude and direction) of the sailboat as observed by the passengers on the oceanliner. 127 You are a pilot on an aircraft carrier. You must fly to another aircraft carrier, now 1450 km at a bearing of 45 0 of your position, moving at 56 km/h due east. The wind is blowing from the south at 72 km/h. Calculate the heading and air speed needed to reach the carrier 2.5 h after you take off. Hint: Draw a displacement vector diagram. 123 A yacht can travel at a speed of 3.33 mls relative to the water. The captain wishes to reach a marina that is 3.00 km directly across the river from his location. The water is flowing at a speed of 1.11 m/s. At what angle (measured upstream relative to the perpendicular line crossing the river) must the captain steer the boat to reach his destination? 128 Refer to Problems and Solutions Manual; 580 km/h, 54 0 east of north A robin is flying south (180 0 ) for the winter at a rate of 40 miles per hour when it runs into a hurricane blowing due west (270 0 ) at 100 miles per hour. What is the new velocity of the robin relative to the ground? upstream A boat that can travel at 4 km/h in still water crosses a river with a current of 2 km/h. At what angle must the boat be pointed upstream (i.e., relative to its actual path) to go straight across the river miles per hour The pilot of an airplane wishes to reach a point 300 km east of the starting point. To avoid a storm area, the pilot decides to proceed to the destination in two hops. On the first hop, the pilot flies due northeast and on the second hop due south. (a) How many kilometers should be flown to the northeast? (b) How many kilometer southward? 125 A man points his rowboat north from A to B, straight across a river of width 100 m. The river flows due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. (a) What is the speed of the river? (b) While the man is crossing the river, what is his velocity relative to the shore? 130 a 424 km b 300 km A weather station releases a weather balloon. The balloon's buoyancy causes it to travel straight up at 1500 m. At the same time, a wind displaces it horizontally 650 m. What is the magnitude and direction (with reference to the horizontal) of the resultant displacement? 126 (a) m/s (b) m/s A 42-km/h wind blows toward 215 0, while a plane heads foward at 152 km/h. What is the resultant velocity of the plane? 1600 m/s (up from horizontal) 160 km/h 140 0

18 131 A bank in downtown Boston is robbed (see the map ). To elude police, the robbers escape by helicopter, making three successive flights described by the following displacements: 32 km, 45 0 south of east; 53 km, 26 0 north of west; 26 km, 18 0 east of south. At the end of the third flight they are captured. In what town are they apprehended? (Use the geometrical method to add these displacements on the map.) 134 On planet Zed the acceleration is 3.6 m/s 2. If an object is placed on a frictionless incline plane, what is the acceleration of the object? 135 A skier squats low and races down a 180 ski slope. During a 5 s interval, the skier accelerates at 2.5 m/s 2. What are the horizontal (perpendicular to the direction of free 2.4 m/s m/s A man is pulling on his 20 kg dog with a force of 70.0 N directed at an angle of above the horizontal. (a) Draw a free body diagram of the forces on the dog. (b) Find the x component of this force. (c) Find the y component of this force. (d) Find the normal force on the dog A trunk is placed on an incline plane that forms a 66 0 angle with the horizontal. Calculate the perpendicular and parallel accelerations m/s parallel 8.95 m/s perpendicular A 25 kg block slides down a 250 incline plane with a constant acceleration. The block starts from rest at the top. At the bottom its velocity reaches 0.65 m/s. The length of the incline is 1.6 meters. (a) Use kinematic formulas to determine the acceleration of the block. (b) Use vector geometry to determine the acceleration down the ramp. (c) Are the two values equal? If not explain why. 137 (a) Drawing (b) 60.6 N (c) 35.0 N (d) N A gardener pushes a 10 kg lawn mower by applying a force of 150 N along the handle. (a) Draw a free body diagram (b) Find the horizontal component of this force when the lawn mower handle makes an angle of (c) Find the horizontal component of this force when the lawn mower handle makes an angle of 45 0 (d) Find the horizontal component of this force when the lawn mower handle makes an angle of 60 o with the horizontal. (a).13 m/s 2 (b) (c) Yes (a) (b) 130 N (c) 106 N (d) 75.0 N

19 138 Joe pushes on the handle of a 10-kg lawn spreader. The handle makes a 45 0 angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5 s. (a) Draw a free body diagram. (b) What is the normal force on the spreader? (c) What force must Joe apply to the handle? Neglect friction. (class) 140 A student pulls a 125 kg box across a floor by means of a rope making an angle of 60 0 with the horizontal. He applies a 60 N force on the rope (a) What is the component of the force in the horizontal direction? (b) What is the component of the force in the vertical direction? (c) What is the normal force on the box? (d) If the angle of the rope is reduced to 30 0 and the same force applied, what will now be the magnitudes of the horizontal, vertical components and the normal force on the box? (a) (b) 107.2N (c) 13 N 139 Wendy pushes a 15 kg lawn spreader across a lawn by applying a force of 95 N along the handle that makes an angle of with the horizontal. (a) Draw a free body diagram. (b) What are the horizontal and vertical components of the force? (c) What is the normal force on the spreader? (d) The handle is lowered so it makes an angle of with the horizontal. Now what are the horizontal and vertical components of the force? (e) What is the new normal force on the spreader? 141 (a) H= 30 N (b) V= 52 N (c) N (d) Hcomp. 52 N Vcomp 30 N Fnormal A 5-kg block is held at rest against a vertical wall by a horizontal force of 100 N. (a) What is the frictional force exerted by the wall on the block? (b) What is the minimum horizontal force needed to prevent the block from falling if the coefficient of friction between the wall and the block is? s = 0.40? (a) (b) horizontal = 48 N, vertical = 82 N (c) (d) horizontal = 82 N, vertical = 48 N (e) (a) N (b) 123 N 142 A student moves a box of books by attaching a rope to the box and pulling with a force of N at an angle of The box of books has a mass of 20.0 kg and the coefficient of kinetic friction between the bottom of the box and the sidewalk is Find the acceleration of the box 1.24 m/s 2 to the right

20 143 A box of books weighing 325 N moves with a constant velocity across the floor when it is pushed with a force of 425 N exerted downward at an angle of below the horizontal. Find? k between the box and the floor. 147 Rachel pulls her 18-kg suitcase at a constant speed by pulling on a handle that makes an angle A with the horizontal. The frictional force on the suitcase is 27 N and Rachel exerts a 43- N force on the handle. (a) What angle does the handle make with the horizontal? (b) What is the normal force exerted on the suitcase? A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 185 N at an angle of 25 0 above the horizontal. The box has a mass of 35 kg, and µ k between box and floor is Find the acceleration of the box. 2.7 m/s (a) 51 0 (b) 143 N, up A 3.00 kg block starts from rest at the top of a incline and slides 2.00 m down the incline in 1.50 s. (a) Find the acceleration of the block. (b) Find the coefficient of kinetic friction between the block and the incline. (c) Find the frictional force acting on the block. (d) Find the speed of the block after it has slid a distance of 2.00 m. 145 A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of with the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s. Determine the coefficient of kinetic friction between the block and the ceiling. (a) 1.78 m/s 2 (b) 0.37 (c) 9.4 N (d) 2.67 m/s 149 The coefficient of static friction between the 3.00 kg crate and the incline of the figure shown below is What is the minimum force, F N that must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? (challenge) A brick layer applies a force of 100 N to each of two handles of a wheelbarrow. Its mass is 20 kg and it is loaded with 30 bricks, each of mass 1.5 kg. The handles of the wheelbarrow are 30 0 from the horizontal and the coefficient of friction is What initial acceleration is given the wheelbarrow? (challenge) 32.1 N 0.71 m/s

21 150 The most massive car ever built was the official car of the General Secretary of the Communist Party in the former Soviet Union. The car had a mass of 3,335 kg. Suppose this car is moving down a slope when the driver applies the brakes. The wheels stop rotating, and the car slides, decelerating at a rate of 6.00 m/s 2. (a) Calculate the force of kinetic friction acting on the car as it decelerates. (b) Determine the coefficient of kinetic friction. 153 A 5.0 kg block on an inclined plane is acted upon by a horizontal force of 50 N shown in the figure below. The coefficient of friction between block and plane is (a) What is the acceleration of the block if it is moved up the plane? (b) How far up the plane will the block go if it has an initial upward speed of 4.0 m/s? (c) What happens to the block after it reaches the highest point? 25,682 N Walter Arfeuille of Belgium lifted a kg load off the ground using his teeth. Suppose Arfeuille can hold three times that mass on a slope using the same force. What is the coefficient of static friction between the load and the slope? (class Problem) 0.2 (a) m/s 2 (b) 3.83 m (c) stops 152 In 1994, a 3.00 x 10 3 kg pancake was cooked, and flipped, in Manchester, England. (a) If the pancake is placed on a surface that is inclined with respect to the horizontal, what must the coefficient of kinetic friction be in order for the pancake to slide down the surface with a constant velocity? (b) What would be the frictional force acting on the pancake? 154 A 3.00 kg block starts from rest at the top of a incline and slides 2.00 m down the incline in 1.50 s. (a) Find the acceleration of the block. (b) Find the coefficient of kinetic friction between the block and the incline. (c) Find the frictional force acting on the block. (d) Find the speed of the block after it has slid a distance of 2.00 m x 10 4 N (a) 1.78 m/s 2 (b) 0.37 (c) 9.4 N (d) 2.67 m/s