A basketball player, standing near the basket to grab a rebound, jumps 76.0 cm vertically.

1 2 A stone is dropped from the edge of a cliff. (a) What is its velocity 3 seconds later? (b) How far does it fall in this time? (c) How far will it fall in the next second of its descent? (a) -29.4 m/sec -96. ft/sec (b) -44.1 m or -144 ft (c) 34.4 m or -112 ft A body in free fall reaches the ground in 5 seconds. (a) From what height in meters was the body dropped? (b) What is the body's final velocity? (c) How far did the body fall in the last second of its descent? (a) +122.5 meters (b) -49 m/sec (c) -44 m 6 7 A basketball player, standing near the basket to grab a rebound, jumps 76.0 cm vertically. (a) How much (total) time does the player spend in the top 15.0 cm of this jump (b) How much (total) time does the player spend in the bottom 15.0 cm? (c) Does this help explain why such players seem to hang in the air at the tops of their jumps? Hard (a) 350 ms (b) 82.0 ms (c) A package in an airplane moving horizontally at 150 m/s is dropped when the altitude is 490 m. (a) How long does it take the package to fall to the ground? (b) How far forward from the spot over which it was dropped does the package land? (c) What kind of path does the package follow? 3 A hoodlum throws a stone vertically downward with an initial speed of 12.0 m/s from the roof of a building, 30.0 m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact? (a) 10 sec (b) 1.5 x 10 3 m (c) parabola 4 5 (a) 1.54 s (b) 27.1 m/s A ball is thrown vertically downward with a velocity of 12 m/sec. (a) How far has the ball fallen 1 second later? (b) How far has the ball fallen 2 seconds after it is first thrwon? (a) -16.9 m (b) -43.6 m A startled armadillo leaps upward, rising 0.544 m in 0.200 s. (a) What was its initial speed? (b) What is its speed at this height? (c) How much higher does it go? 8 9 A stone is thrown horizontally at a speed of + 5.0 m/s from the top of a cliff 78.4 m high. (a) How long does it take the stone to reach the bottom of the cliff? (b) How far from the base of the cliff does the stone strike the ground? (c) What are the horizontal and vertical components of the velocity of the stone just before it hits the ground? (a) 4.0 s (b) 20 m (c) v x = 5.0 m/s v y = 39.2 m/s A steel ball rolls with constant velocity across a tabletop 0.950 m high. It rolls off and hits the ground +0.352 m horizontally from the edge of the table. How fast was the ball rolling? 0.800 m/s Hard (a) 3.70 m/s (b) 1.74 m/s (c) 0.154 m higher 10 A movie director is shooting a scene that involves dropping a stunt dummy out of an airplane and into a swimming pool. The plane is 10.0 m above the ground, traveling at a velocity of 22.5 m/s in the positive x direction. The director wants to know where in the plane s path the dummy should be dropped so that it will land in the pool. 32.2 m

11 A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way and the cat slides off the table at a speed of 5.0 m/s. Where does the cat strike the floor? 18 The world's highest suspension bridge is the Royal Gorge Bridge in Colorado. The bridge spans the top of the gorge, which rises 321 m above the Arkansas River. Suppose you kick a little rock horizontally off the bridge. The rock hits the water so that the magnitude of its horizontal displacement is 45.0 m. Find the speed at which the rock was kicked. 2.2 m from the table 12 An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 100.0 m/s at a height of 50.0 m above the ground. What horizontal distance does the package travel before striking the ground? 319 m 19 5.56 m/s The longest banana split ever made was 7.32 km long (needless to say, more than one banana was used). If an archer were to shoot an arrow horizontally from the top of Mount Everest, which is located 8848 m above sea level, would the arrow's horizontal displacement be larger than 7.32 km? Assume that the arrow cannot be shot faster than 100.0 m/s, that there is no air resistance, and that the arrow lands at sea level. 13 During a thunderstorm, a tornado lifts a car to a height of 125 m above the ground. Increasing in strength, the tornado flings the car horizontally with an initial speed of 90.0 m/s. (a) How long does the car take to reach the ground? (b) How far horizontally does the car travel before hitting the ground? Doesn t make it 172 m/s (a) 5.05 s (b) 454 m 20 The world's largest flowerpot is 1.95 m high. If you were to jump horizontally from the top edge of this flowerpot at a speed of 3.0 m/s, what would your landing speed be? 14 A bullet is fired horizontally from a pistol, and another bullet is dropped simultaneously from the same height. Neglecting air resistance, which bullet hits the ground first? both hit at the same time 21 6.87 m/s The longest stuffed toy ever manufactured is a 420 m snake made by Norwegian children. Suppose a projectile is thrown horizontally from a height half the length of the snake and the projectile's horizontal displacement is as long as the snake. What would be the projectile's initial speed? 15 Does a ball dropped out of the window of a moving car take longer to reach the ground than one dropped at the same height from a car at rest? (Neglect air resistance) 64 m/s 16 no, neglecting air resistance A rock is dropped at the same instant that a ball at the same elevation is thrown horizontally. Which will have the greater velocity when it reaches ground level? 22 Libyan basketball player Suleiman Nashnush was the tallest basketball player ever. His height was 2.45 m. Suppose Nashnush throws a basketball horizontally from a level equal to the top of his head. If the speed of the basketball is 12 m/s when it lands, what is the ball's initial speed? (Hint: Consider the components of final velocity.) 9.8 m/s 17 Both vertical velocities will be the same, but the thrown ball will have a greater net velocity. The fastest recorded pitch in Major League Baseball, thrown by Nolan Ryan in 1974, was clocked at 162.3 km/h (100.8 mi/h). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 18.3 m (60.0 ft) away? 23 The longest shot made during a golf tournament was made by Michael Austin in 1974. The ball went a distance of 471 m. Suppose the ball was shot horizontally off a cliff at 80.0 m/s. Calculate the height of the cliff. the cliff is 1.70 x 10 2 m high 0.809

24 Florence Griffith-Joyner of the United States set the women's world record for the 200 m run by running with an average speed of 9.28 m/s. Suppose Griffith-Joyner wants to jump over a river. She runs horizontally from the river's higher bank at 9.28 m/s and lands on the edge of the opposite bank. If the difference in height between the two banks is 2.00 m, with the far bank having the lower height, how wide is the river? 29 An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 100.0 m/s at a height of 50.0 m above the ground. Find the velocity (magnitude and direction) of the package just before it hits the ground. 5.93 m 104.8 m/s 17.4 0 below the horizontal 72.6 0 from the vertical 25 Elmer Trett, in 1994 reached a speed of 372 km/h on his motorcycle. If Trett drives off a horizontal ramp at this speed and lands a horizontal distance of 40.0 m away from the edge of the ramp, what is the height of the ramp? Neglect air resistance. 30 A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 35 m/s. The cliff is 52 m above the water s surface. (a) How long does it take for the stone to fall to the water? (b) With what speed does it strike the water? 26 The ramp is 0.740 m high A Snorkel fire engine is designed for putting out fires that are well above street level. The engine has a hydraulic lift that lifts the firefighter and a system that delivers pressurized water to the firefighter. Suppose that the engine cannot move closer than 25 m to a building that has a fire on its eighth floor, which is 25 m above street level. If the horizontal speed of the water emerging from the hose is 15 m/s, how high above the street must the firefighter be lifted in order for the water to reach the fire. 39 m 31 3.258 s, 47 m/s In the figure, a rescue plane flies at 198 km/h (= 55.0 m/s) and a constant elevation of 500 m toward a point directly over a boating accident victim struggling in the water very close to the victim. (a) What should be the angle θ of the pilot's line of sight to the victim when the release is made? (b) As the capsule reaches the water, what is its velocity v in unit-vector notation? (c) As the capsule reaches the water, what is its velocity v in magnitude-angle notation? 27 A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 18 m/s. The cliff is 52 m above the water s surface, as shown in the figure below. (a) How long does it take for the stone to fall to the water? (b) With what speed does it strike the water? (a) 3.3 s, (b) 36 m/s (a) (b) (c) 28 A pelican flying along a horizontal path drops a fish from a height of 5.4 m while traveling 5.0 m/s. Give both the horizontal and vertical components of the velocity of the fish before the fish enters the water. v h = 5.0 m/s v v = 10.2 m/s

32 The figure shows a pirate ship 560 m from a fort defending the harbor entrance of an island. A defense cannon, located at sea level, fires balls at initial speed v 0 = 82 m/s. (a) At what angle θ 0 from the horizontal must a ball be fired to hit the ship? (b) How far should the pirate ship be from the cannon if it is to be beyond the maximum range of the cannonballs? 35 Which of the following exhibit parabolic motion? (a) a flat rock skipping across the surface of a lake (b) a three-point shot in basketball (c) the space shuttle while orbiting Earth (d) a ball bouncing across a room (e) a cliff diver (f) a life preserver dropped from a stationary helicopter (g) a person skipping (a) (b) (c) (d) (e) (f) (g) (a) (b) 36 A projectile is launched with an initial speed of 30 m/s at an angle of 60 0 above the horizontal. (a) Calculate the magnitude and direction of its velocity 2.0 s after launch. (b) Calculate the magnitude and direction of its velocity 5.0 s after launch. 33 A projectile is launched with an initial speed of 30 m/s at an angle of 60 0 above the horizontal. (a) What is the magnitude of its velocity 2.0 s after launch? (b) What is the angle of its velocity 2.0 s after launch? (c) What is the angle above or below the horizontal? (d) What is the magnitude of its velocity 5.0 s after launch? (e) What is the angle of its velocity 5.0 s after launch? (f) Is the angle above or below the horizontal? 37 (a) 23 degrees 16.4 m/s (b) 56.89 0 degrees 27.5 m/s Streams of water in a fountain shoot from one level to the next. A particle of water in a stream takes 0.50 s to travel between the first and second level. The receptacle on the second level is a horizontal distance of 1.5 m away from the spout on the first level. If the water is projected at an angle of 33 0, what is the initial speed of the particle? 34 (a) 16 m/s (b) 23 0 (c) above (d) 27 m/s (e) 57 0 (f) below Which of the following are examples of projectile motion? (a) an airplane taking off (b) a tennis ball lobbed over a net (c) a plastic disk sailing across a lawn (d) a hawk diving to catch a mouse (e) a parachutist drifting to Earth (f) a frog jumping from land into the water b f 38 39 3.6 m/s If a water particle in a stream of water in a fountain takes 0.35 s to travel from spout to receptacle when shot at an angle of 67 0 and an initial speed of 5.0 m/s, what is the vertical distance between the levels of the fountain? 1.0 m A ball is fired from the ground with an initial speed of 1.70 x 10 3 m/s (approximately five times the speed of sound) at an initial angle of 55.0 0 Above the horizontal. Neglect air resistance, (a) Find the ball s horizontal range. (b) Find the amount of time the ball is in motion. (a) 277, 113 m (b) 284 s

40 A shell is fired at an angle of 40 degrees above the horizontal at a velocity of 300 m/sec. (a) What is the shell's range one second into the flight (b) What is the shell's time of flight (c) What is the shell's total range? 46 A diver takes off from a 10 meter high diving board at an angle of 60 degrees above the horizontal and with a speed of 15 m/s. (a) How long is he in the air (b) What is the maximum height the diver reaches above the water? (c) What is the diver's range? (d) What is the diver's observed speed just before he enters the water. 41 (a) 229.8 m (b) 39.34 sec (c) 9,044 m A bullet is fired from a gun at 30 degree angle above the horizontal and a muzzle velocity of 600 m/sec. What is the range of the gun for this angle of elevation? (a) 3.28 s (b) 18.6 m (c) 24.6 m (d) 20.5 m/s 42 3.18 x 10 4 m An arrow is shot at a 30.0 0 angle above the horizontal. It has a velocity of 49 m/s. (a) How high will the arrow go? (b) What horizontal distance will it travel? 47 In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at an angle of 15 0 with respect to the flat roof while traveling at a speed of 5.0 m/s. Will he make it to the other roof, which is 0.5 m shorter than the building he jumps from? No y = -2.3 m 43 (a) 30.6 m (b) 212 m Trailing by two points, and with only 2.0 s remaining in a basketball game, a player makes a jump-shot at an angle of 60 0 with the horizontal, giving the ball a velocity of 10 m/s. The ball is released at the height of the basket, 3.05 m above the floor. Yes! It's a score. (a) How much time is left in the game when the basket is made? (b) Shots made outside a semicircle of 6.02-m radius from a spot directly beneath the basket are awarded 3 points, while those inside score 2 points. Did the player tie the game or put the team ahead? 48 49 A golfer can hit a golf ball a horizontal distance of over 300 m on a good drive. What maximum height would a 301.5 m drive reach if it were launched at an angle of 25.0 0 to the ground? (Hint: At the top of its flight, the ball s vertical velocity will be zero.) 34.9 m Salmon often jump waterfalls to reach their breeding grounds. Starting 2.00 m from a waterfall 0.55 m in height, at what minimum speed must a salmon jumping at an angle of 32.0 0 leave the water to continue upstream? (a) 0.25 s (b) ahead 6.2 m/s 44 A basketball player tries to make a half-court jump-shot, releasing the ball at the height of the basket. Assuming the ball is launched at 51.0 0, 14.0 m from the basket, what velocity must the player give the ball? 50 A quarterback throws the football to a receiver who is 31.5 m down the field. If the football is thrown at an initial angle of 40.0 0 to the ground, at what initial speed must the quarterback throw the ball? What is the ball s highest point during its flight? 11.8 m/s 51.0 o 17.7 m/s 6.60 m 45 A golf ball is hit with a velocity of 24.5 m/s at 35 0 above the horizontal. (a) Find the range of the ball. (b) Find the maximum height of the ball. (a) 57.9 m (b) 10.2 m

51 A daredevil is shot out of a cannon at 45.0 0 to the horizontal with an initial speed of 25.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil? 56 The narrowest strait on Earth is Seil Sound, in Scotland, which lies between the mainland and the island of Seil The strait is only about 6.0 m wide. Suppose an athlete wanting to jump "over the sea" leaps at an angle of 35 0 with respect to the horizontal. What is the minimum initial speed that would allow the athlete to clear the gap? Neglect air resistance. 10.7 m 7.9 m/s 52 A place kicker must kick a football from a point 36.0 m (about 40.0 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53 0 to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling? 57 In 1993, Wayne Brian threw a spear a record distance of 201.24 m. (This is not an official sport record because a special device was used to "elongate" Brian's hand.) Suppose Brian threw the spear at a 35.0 0 angle with respect to the horizontal. What was the initial speed of the spear? 45.8 m/s 53 (a) clears the goal by 1 m (b) falling A ball player hits a home run, and the baseball just clears a wall 21.0 m high located 130.0 m from home plate. The ball is hit at an angle of 35.0 0 to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.0 m above the ground. (a) What is the initial speed of the ball? (b) How much time does it take for the ball to reach the wall? (c) Find the velocity components and the speed of the ball when it reaches the wall. Hard 58 59 In 1989 during overtime in a high school basketball game in Erie, Pennsylvania, Chris Eddy threw a basketball a distance of 27.5 m to score and win the game. If the shot was made at a 50.0 0 angle above the horizontal, what was the initial speed of the ball? 16.6 m/s A scared kangaroo once cleared a fence that was 2.44 m high. If the horizontal component of the kangaroo's velocity was 4.80 m/s, Find the angle with respect to the ground at which the kangaroo leaped. 54 55 (a) 41.7 m/s (b) 3.81 s (c) v yf = -13.5m/s, v xf = 34.2 m/s, v f = 36.7 m/s A daredevil jumps a canyon 12 m wide. To do so, he drives a car up a 15 0 incline. (a) What minimum speed must he achieve to clear the canyon? (b) If the daredevil jumps at this minimum speed, what will his speed be when he reaches the other side? Hard (a) 15.34 m/s (b) -15.34 m/s A 2.00 m tall basketball player attempts a goal 10.0 m from the basket (3.05 m high). If he shoots the ball at a 45.0 0 angle, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? 104 m/s 60 61 55.2 0 In 1991, Doug Danger rode a motorcycle to jump a horizontal distance of 76.5 m. Find the maximum height of the jump if his angle with respect to the ground at the beginning of the jump was 12.00. 4.07 m A stone is catapulted rightward with an initial velocity of 20.0 m/s at an angle of 40.0 0 above level ground. (a) Find its horizontal and vertical displacements 1.10 s after launch. (b) Find its horizontal and vertical displacements 1.80 s after launch. (c) Find its horizontal and vertical displacements 5.00 s after launch. (a) 8.21 m (b) 7.26 m (c) 40.1 m

62 A certain airplane has a speed of 290.0 km/h and is diving at an angle θ 0 = 30.0 0 below the horizontal when the pilot releases a radar decoy (see the figure). The horizontal distance between the release point and the point where the decoy strikes the ground is d = 700 m. (a) How long is the decoy in the air? (b) How high was the release point? 65 A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45 0. A player 55 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? 5.8 m/s 66 A baseball leaves a pitcher's hand horizontally at a speed of 161 km/h. The distance to the batter is 18.3 m. (a) How long does the ball take to travel the first half of that distance? (b) How long does the ball take to travel second half? (c) How far does the ball fall freely during the first half? (d) How far does the ball fall freely during the second half? (e) Why aren't the quantities in (c) and (d) equal? (a) 10.0 s; (b) 897 m 63 During a tennis match, a player serves the ball at 23.6 m/s, with the center of the ball leaving the racquet horizontally 2.37 m above the court surface. The net is 12 m away and 0.90 m high. (a) When the ball reaches the net, does the ball clear it? (b) If the ball clears the net what is the distance between the center of the ball and the top of the net? Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00 0 below the horizontal. (c) When the ball reaches the net, does the ball clear it? (d) If the ball clears the net what is the distance between the center of the ball and the top of the net? (a) yes; (b) 20 cm; (c) no; (d) 86 cm 67 (a) 0.205 s; (b) 0.205 s; (c) 20.5 cm; (d) 61.5 cm In the figure a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.50 s later, at distance d = 25.0 m from the building and at angle θ = 60.0 0 with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) (b) What is the magnitude relative to the horizontal of the velocity at which the ball is thrown? (c) What is the angle relative to the horizontal of the velocity at which the ball is thrown? (d) Is the angle above or below the horizontal? 64 A plane, diving with constant speed at an angle of 53.0 0 with the vertical, releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after release. (a) What is the speed of the plane? (b) How far does the projectile travel horizontally during its flight? (c) What is the horizontal components of its velocity just before striking the ground? (d) What is the vertical components of its velocity just before striking the ground? (a) 32.2m; (b) 21.9m/s; (c) 40.4 0 ; (d) below the horizontal. (a) 202 m/s; (b) 806 m; (c) 161m/s; (d) -171m/s

68 A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in the figure, where t = 0 at the instant the ball is struck. (a) How far does the golf ball travel horizontally before returning to ground level? (b) What is the maximum height above ground level attained by the ball? 70 In the figure, a ball is thrown up onto a roof, landing 4.00 s later at height h = 20.0 m above the release level. The ball's path just before landing is angled at θ = 60.0 0 with the roof. (a) Find the horizontal distance d it travels. (b) What is the magnitude (relative to the horizontal) of the ball's initial velocity? (c) What is the angle (relative to the horizontal) of the ball's initial velocity? 69 (a) 95 m; (b) 31m In the figure, a ball is launched with a velocity of magnitude 10.0 m/s, at an angle of 50.0 0 to the horizontal. The launch point is at the base of a ramp of horizontal length d 1 = 6.00m and height d 2 = 3.60 m. A plateau is located at the top of the ramp. (a) Does the ball land on the ramp or the plateau? (b) When it lands, what is themagnitude of its displacement from the launch point? (c) When it lands, what is the angle of its displacement from the launch point? 71 (a) 33.7 m; (b) 26.0 m/s; (c) 71.1 0 A ball rolls horizontally off the top of a stairway with a speed of 1.52 m/s. The steps are 20.3 cm high and 20.3 cm wide. Which step does the ball hit first? the third (a) it lands on the ramp; (b) 5.82 m; (c) 31.0 0 72 Two seconds after being projected from ground level, a projectile is displaced 40 m horizontally and 53 m vertically above its launch point. (a) What is the horizontal components of the initial velocity of the projectile? (b) What is the vertical components of the initial velocity of the projectile? (c) At the instant the projectile achieves its maximum height above ground level, how far is it displaced horizontally from the launch point? (a) 20 m/s; (b) 36 m/s; (c) 74 m

73 You are to throw a ball with a speed of 12.0 m/s at a target that is height h = 5.00 m above the level at which you release the ball (see the figure). You want the ball's velocity to be horizontal at the instant it reaches the target. (a) At what angle θ above the horizontal must you throw the ball? (b) What is the horizontal distance from the release point to the target? (c) What is the speed of the ball just as it reaches the target? 76 A baseball is hit at Fenway Park in Boston at a point 0.762 m above home plate with an initial velocity of 33.53 m/s directed 55.0' above the horizontal. The ball is observed to clear the 11.28-m-high wall in left field (known as the "green monster") 5.00 s after it is hit, at a point just inside the leftfield foul-line pole. (a) Find the horizontal distance down the left-field foul line from home plate to the wall; (b) Find the vertical distance by which the ball clears the wall; the (c) Find horizontal displacements of the ball with respect to home plate 0.500 s before it clears the wall. (d) Find vertical displacements of the ball with respect to home plate 0.500 s before it clears the wall. (a) 96.2m; (b) 4.31 m; (c) 86.5 m forward; (d) 25.1 m up 74 (a) 55.6 0 ; (b) 6.85 m; (c) 6.78 m/s In a detective story, a body is found 4.6 m from the base of a building and 24 m below an open window. (a) Assuming the victim left that window horizontally, what was the body's initial speed? (b) Would you guess the death to be accidental? Explain your answer. 77 A ball is fired with an initial speed of 1.70 x 10 3 m/s (approximately five times the speed of sound) at an initial angle of 55.0 0 below the horizontal. Neglect air resistance. (a) Find the ball s horizontal range.if it is in the air 5 seconds. (b) What is the ball s horizontal velocity at 5 seconds? (c) What is the ball s vertical velocity at 5 seconds? (d) What is the ball s final velocity at 5 seconds? (make sure you give both the angle and direction. (e) What was the ball s height at the start? 75 (a) 2.1 m/s; (b) not accidental because horizontal launch speed is about 20% of world class sprint speed A helicopter is flying in a straight line over a level field at a constant speed of 6.2 m/s and at a constant altitude of 9.5 m. A package is ejected horizontally from the helicopter with an initial velocity of 12 m/s relative to the helicopter and in a direction opposite the helicopter's motion. (a) Find the initial speed of the package relative to the ground. (b) What is the horizontal distance between the helicopter and the package at the instant. the package strikes the ground? (c) What angle does the velocity vector of the package make with the ground at the instant before impact, as seen from the ground? (a) 5.8 m/s; (b) 17 m; (c) 67 0 78 79 (a) (b) (c) (d) (e) A projectile is launched with an initial speed of 30 m/s at an angle of 60 0 below the horizontal. (a) Calculate the magnitude and direction of its velocity 2.0 s (b) Calculate the magnitude and direction of its velocity 5.0 s after launch. (a) (b) A projectile is shot downward at a 60 degree angle with the horizontal and a speed of 200 m/sec. (a) Obtain the vertical component of its velocity (b) Obtain the horizontal components of it velocity (c) How far has the projectile gone horizontally at the end of the first 4.00 sec.? (a) v v = 173.2 m/s (b) v h = 100 m/s (c) d h = 400 m

80 A bullet is fired from a gun at 30 degree angle below the horizontal and a muzzle velocity of 600 m/sec. What is the range of the gun for this angle of elevation if it is fired from a 20 m high building? 85 You throw a ball from a cliff with an initial velocity of 15.0 m/s at an angle of 20.0 0 below the horizontal. (a) Find its horizontal displacement 2.3 s later.. (b) Find its vertical displacement 2.30 s later. 34.2 m (a) 32.4 m (b) -37.7 m 81 An arrow is shot at a 30.0 o angle below the horizontal. It has a velocity of 49 m/s. and travels for.5 sconds. (a) How far will the arrow drop? (b) What horizontal distance will it travel? (a) (b) 86 An airplane, diving at an angle of 53.0' from the vertical, releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after being released. (a) What is the speed of the aircraft? (b) How far did the projectile travel horizontally during its flight? (c) What were the horizontal and vertical components of its velocity just before striking the ground? 82 A diver takes off from a 10 meter high diving board at an angle of 60 degrees below the horizontal and with a speed of 15 m/s. (a) How long is he in the air (b) What is the maximum height the diver reaches above the water? (c) What is the diver's range? (d) What is the diver's observed speed just before he enters the water. (a).61 s (b) 10 m (c) 4.57 m (d) 20.4 m/s 87 (a) 202 m/s (b) 806 m (c) -171 In a cathode-ray tube, a beam of electrons is projected horizontally with a speed of 1.0 x 10 9 cm/s into the region between a pair of horizontal plates 2.0 cm square. An electric field between the plates causes a constant downward acceleration of the electrons of magnitude 1.0 x 10 17 cm/s 2. (a) Find the time required for an electron to pass through the plates, (b) Find the vertical displacement of the beam in passing through the plates (it does not run into a plate), and (c) Find the velocity of the beam as it emerges from the plates. 83 In a scene in an action movie, a stuntman dives from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at an angle of 15 0 below the horizon with respect to the flat roof while traveling at a speed of 5.0 m/s. Will he make it to the other roof, which is 1.5 m shorter than the building he jumps from? (a) 2.0 ns (b) 0.20 cm (c) 2.0 x 10 8 cm/s. 84 A stone is catapulted rightward with an initial velocity of 20.0 m/s at an angle of 40.0 0 below the horizontal. Find its horizontal and vertical displacements (a) Find its horizontal and vertical displacements 1.10 s after launch. (b) Find its horizontal and vertical displacements 1.80 s after launch. (c) Find its horizontal and vertical displacements 5.00 s after launch. (a) d v = -20.059 m d h = +16.85 m (b) d v = -39 m d h = +27.5 m (c) d v = -187 m d h = +76.6 m 88 89 Michael Hout of Ohio can run 110.0 m hurdles in 18.9 s at an average speed of 5.82 m/s. What makes this interesting is that he juggles three balls as he runs the distance. Suppose Hout throws a ball up and forward at twice his running speed and just catches it at the same level. At what angle, q, must the ball be thrown? (Hint: Consider horizontal displacements for Hout and for the ball.) 60 0 A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the monkey, the zookeeper kneels 10.0 m from the light pole, which is 5.00 m high. The tip of her gun is 1.00 m above the ground. The monkey tries to trick the zookeeper by dropping a banana, then continues to hold onto the lightpole. At the moment the monkey releases the banana, the zookeeper shoots. If the tranquilizer dart travels at 50.0 m/s will the dart hit the monkey or the banana banana 4.77 m above the ground dart 4.76 above the ground

90 If a rock is dropped from the top of a sailboat s mast, will it hit the deck at the same point whether the boat is at rest or in motion at constant velocity? 95 A golf ball with an initial angle of 34 0 lands exactly 240 m down the range on a level course. (a) Neglecting air friction, what initial speed would achieve this result? (b) Using the speed determined in item (a), find the maximum height reached by the ball. yes, neglecting air resistance 91 When a water gun is fired while being held horizontally at a height of 1.00 m above ground level, the water travels a horizontal distance of 5.00 m. A child holds the same gun in a horizontal position while sliding down a 45.00 incline at a constant speed of 2.00 m/s. If the child fires the gun when it is 1.00 m above the ground and the water takes 0.329 s to reach the ground, how far will the water travel horizontally? 4.11 m 96 (a) 5.0 x 10 1 m/s (b) 4.0 x 10 1 m A science student riding on a flatcar of a train moving at a constant speed of 10.0 m/s throws a ball toward the caboose along a path that the student judges as making an initial angle of 60.0 0 with the horizontal. The teacher, who is standing on the ground nearby, observes the ball rising vertically. How high does the ball rise? 92 A ship maneuvers to within 2500 m of an island s 1800 m high mountain peak and fires a projectile at an enemy ship 610 m on the other side of the peak, as illustrated in the figure below. If the ship shoots the projectile with an initial velocity of 250 m/s at an angle of 75 0 ; (a) How close to the enemy ship does the projectile land? (b) How close (vertically) does the projectile come to the peak? 97 15.3 A football is thrown toward a receiver with an initial speed of 18.0 m/s at an angle of 35.0 0 above the horizontal. At that instant, the receiver is 18.0 m from the quarterback. In what direction and with what constant speed should the receiver run to catch the football at the level at which it was thrown? 6.19 m/s downfield 93 (a) 100 m, (b) 100 m A ball is thrown straight upward and returns to the thrower s hand after 3.00 s in the air. A second ball is thrown at an angle of 30.0 0 with the horizontal. At what speed must the second ball be thrown so that it reaches the same height as the one thrown vertically? 98 A rocket is launched at an angle of 53 0 above the horizontal with an initial speed of 75 m/s, as shown in the figure. It moves for 25 s along its initial line of motion with an acceleration of 25 m/s 2. At this time its engines fail and the rocket proceeds to move as a free body. (a) What is the rocket s maximum altitude? (b) What is the rocket s total time of flight? (c) What is the rocket s horizontal range? 29.4 m/s 94 A ball is projected horizontally from the edge of a table that is 1.00 m high, and it strikes the floor at a point 1.20 m from the base of the table. (a) What is the initial speed of the ball? (b) How high is the ball above the floor when its velocity vector makes a 45.0 0 angle with the horizontal? (a) 2.4 x 10 4 m (b) 152 s (c) 6.0 x 10 4 m (a) 2.66 m/s (b) 0.640 m

99 In 1978, Geoff Capes of the United Kingdom won a competition for throwing 5 lb bricks; he threw a brick a distance of 44.0 m. Suppose the brick left Capes' hand at an angle of 45.0 0 with respect to the horizontal. (a) Find the initial speed of the brick. (b) If Capes threw the brick straight up with the speed found in part (a), what is the maximum height the brick could have achieved? 103 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 10.0 0 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. 100 20.8 m/s 22.1 m According to measurements made in 1910, a common flea can jump 0.330 m. Assuming that the flea's initial speed is 2.20 m/s, find the angle with respect to the ground at which the flea leaps. (Hint: Use the trigonometric identity sin q cos q = 1 sin 2q.) Hard 104 S 25,682 N 0.798 Walter Arfeuille of Belgium lifted a 281.5 kg load off the ground using his teeth. Suppose Arfeuille can hold three times that mass on a 30.0 0 slope using the same force. What is the coefficient of static friction between the load and the slope? 21.0 0 S 101 A 3.00 kg block starts from rest at the top of a 30.0 0 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. 105 0.2 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 31.0 0 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? S (a) 1.78 m/s 2 (b) 0.37 (c) 9.4 N (d) 2.67 m/s S 0.601 1.52 x 10 4 N 102 The coefficient of static friction between the 3.00 kg crate and the 35.0 0 incline of the figure shown below is 0.300. 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? S (challenge) 32.1 N

106 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 0.30. (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? S (class Problem) (a) -2.06 m/s 2 (b) 3.83 m (c) stops 107 A diver takes off from a 10 meter high diving board at an angle of 60 degrees above the horizontal and with a speed of 15 m/s. (a) How long is he in the air (b) What is the maximum height the diver reaches above the water? (c) What is the diver's range? (d) What is the diver's observed speed just before he enters the water. (a) 3.28 s (b) 18.6 m (c) 24.6 m (d) 20.5 m/s 108 A bullet is fired from a gun at 30 degree angle below the horizontal and a muzzle velocity of 600 m/sec. What is the range of the gun for this angle of elevation if it is fired from a 20 m high building? 34.2 m