What is the acceleration of a racing car if its velocity is increased uniformly from 44 m/s, south to 66 m/s, south over an 11 second period?


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1 1 What is the acceleration of a racing car if its velocity is increased uniformly from 44 m/s, south to 66 m/s, south over an 11 second period? 7 A car traveling in a straight line has a velocity of +5.0 m/s. After 4.0 s; its velocity is +8.0 m/s. (a) What is the car's average acceleration in this time interval? (b) What is the car s displacement? m/s 2, south An airplane flying at 90 m/s, east is accelerated uniformly at the rate of 0.5 m/s 2, east, for ten seconds. What is its final velocity in: (a) m/s (b) Km/h? s (a) 95 m/s, east, (b) 342 km/h, east 8 (a) +.75 m/s 2 (b) 26 m A car traveling at +7.0 m/s accelerates at the rate of m/s 2 for an interval of 2.0 s. (a) Find v f (b) Find the displacement m/s 15.6 meters 3 A car moving at 10 m/s is uniformly accelerated at the rate of 0.50 m/s 2 (a) Draw a velocity time graph of the motion (b) What is the speed of the car 6.0 s after the acceleration begins? (c) How far does the car move during the 6.0 s? s 9 A snowmobile has an initial velocity of +3.0 m/s. (a) If it accelerates at the rate of m/s 2 for 7.0 s, what is the final velocity? (b) What is its displacement during that time interval? (c) If it accelerates at the rate of m/s 2, how long will it take to come to a complete stop? (d) What is its displacement during that time interval? 4 (a) graphlinear (b) 13 m/s (c) 69 m In 1991 at Smith College, in Massachusetts, Ferdie Adoboe ran backward for a distance of 1.00 x 10 2 m in 13.6 s. Suppose it takes Adoboe 2.00 s to achieve a speed equal to her average speed during the run. Find the magnitude of her average acceleration during the first 2.00 s. (a) +6.5 m/s (b) m (c) 5.0 s (d) 7.2 meters Alternate Interpretation (c) 10.8 s (d) 35.2 m s m/s 2 In 1991, four English teenagers built an electric car that could attain a speed of 30.0 m/s. Suppose it takes 8.0 s for this car to accelerate from 18.0 m/s to 30.0 m/s (a) What is the magnitude of the car's acceleration? (b) What is the displacement of the car? 10 A tennis ball with a velocity of m/s to the right is thrown perpendicularly at a wall. After striking the wall, the ball rebounds in the opposite direction with a velocity of 8.0 m/s to the left. If the ball is in contact with the wall for s, what is the average acceleration of the ball while it is in contact with the wall? (Make sure you draw a picture and sketch a graph s m/s 2 6 (a) 1.5 m/s 2 (b) 192 m Capt. Charles Yeager performed the first supersonic flight in He flew at a speed of 3.00 x 10 2 m/s at an altitude of more than 12 km, where the speed of sound in air is slightly less than 3.00 x 10 2 m/s. Suppose Capt. Yeager accelerated from 1.20 x 10 2 m/s to 3.00 x 10 2 m/s in 25.0 s. What was the magnitude of his acceleration? s 11 As a shuttle bus comes to a normal stop, it slows from 9.00 m/s to 0.00 m/s in 5.00 s. (Draw a Velocity Time Graph and list the information) (a) Find the average acceleration of the bus. (b) Find the displacement of the bus. (a) m/s 2 (b) 22.5 m 7.20 m/s 2
2 12 When A shuttle bus comes to a sudden stop to avoid hitting a dog, it slows from 9.00 m/s to 0.00 m/s in 1.50 s. (Draw a Velocity Time Graph and list the information) (a) Find the average acceleration of the bus. (b) Find the displacement of the bus. 17 An amusement park ride that falls from rest to a speed of 28 m/s in 3.0 s. (Draw a Velocity Time Graph and list the information) (a) Find the acceleration of the amusement park ride. (b) How far does it travel in the 3.0 seconds? (a) m/s 2 (b) 6.75 m (a) 9.3 m/s 2 (b) 13 A car traveling initially at 7.0 m/s accelerates to a velocity of 12.0 m/s in 2.0 s. (Draw a Velocity Time Graph and list the information) (a) Find the average acceleration of the bus. (b) Find the displacement of the bus. 18 A motorcycle with an average acceleration of 15 m/s 2 reaches a velocity of 27 m/s from rest. (Draw a Velocity Time Graph and list the information) (a) How long does it take? (b) How far does it travel when it reaches that velocity? (a) 2.5 m/s 2 (b) 19 m (a) 1.8 seconds (b) 14 Turner s treadmill starts with a velocity of 1.2 m/s and speeds up at regular intervals during a half hour workout. After 25 minutes, the treadmill has a velocity of 6.5 m/s. (Draw a Velocity Time Graph and list the information) (a) What is the average acceleration of the treadmill during this period? (b) What is the displacement of the treadmill during this period 19 A sports car with an average acceleration of 5.1 m/s 2 reaches a velocity of 27 m/s from rest. (Draw a Velocity Time Graph and list the information) (a) How long does it take? (b) How far does it travel when it reaches that velocity? (a) 5.3 seconds (b) m 15 (a) 3.5 x103 m/s 2 (b) m If a treadmill starts at a velocity of 2.7 m/s and has a velocity of 1.3 m/s after 5.0 min. (Draw a Velocity Time Graph and list the information) (a) What is the average acceleration of the treadmill? (b) Find the displacement of the treadmill 20 A bicyclist accelerates from 5.0 m/s to a velocity of 16 /s in 8 s. (Draw a Velocity Time Graph and list the information) (a) Assuming constant acceleration, what distance does the bicyclist travel during this interval? (b) What is his acceleration during this time interval? (a) 84 m (b) 1.38 m/s 2 16 (a) 4.7 x 103 m/s 2 (b) 600 m A cyclist has an initial velocity of 13.5 m/s and an acceleration of m/s 2. (Draw a Velocity Time Graph and list the information) (a) How long will it take a cyclist to bring a bicycle to a complete stop? (b) How far did the bicyclist travel when he came to a complete stop? 21 While a baseball is being hit, its speed changes from 35 m/s to +52 m/s in a time interval of 0.10 s. (Draw a Velocity Time Graph and list the information (a) Assuming constant acceleration, what is the ball s displacement during this time interval? (b) What is the path length of the baseball during this time interval (c) What is the acceleration of the baseball? (a) 27 s (b) m (a).85 m (b) (c)
3 22 John Howard of the United States reached the highest speed ever achieved on a bicycle. The bicycle, which was accelerated by being towed by a vehicle, reached a speed of 245 km/h. Suppose Howard wants to slow down and applies the brakes on his now freely moving bicycle. If the average deceleration of the bicycle has a magnitude of 3.00 m/s 2, how long will it take for the bicycle's speed to decrease by 20.0 percent? 27 When Maggie applies the brakes of her car, the car slows uniformly from m/s to 0.00 m/s in 2.50 s. (Draw a Velocity Time Graph and list the information) (a) How many meters before a stop sign must she apply her brakes in order to stop at the sign? (b) What is her acceleration? 4.57 s (a) 18.8 m (b) 6 m/s 2 23 A boy sledding down a hill accelerates at 1.40 m/s 2. If he started from rest, in what distance would he reach a speed of 7.00 m/s? 28 A jet plane lands with a velocity of +100 m/s and can accelerate at a maximum rate of 5.0 m/s 2 as it comes to rest. Can this plane land at an airport where the runway is 0.80 km long? (Draw a Velocity Time Graph and list the information) 17.5 m No; the plane needs 1 km to land. 24 The polar bear is an excellent swimmer, and it spends a large part of its time in the water. Suppose a polar bear wants to swim from an ice floe to a particular point on shore where it knows that seals gather. The bear dives into the water and begins swimming with a speed of 2.60 m/s. By the time it arrives at the shore, its speed has decreased to 2.20 m/s. If the polar bear's swim takes exactly 9.00 min. and it has a constant deceleration, what is the distance traveled by the polar bear? m 29 note.058 hr.1086 km/hr A driver in a car traveling at a speed of 78 km/h sees a cat 100 m away on the road. (Draw a Velocity Time Graph and list the information) (a) How long will it take for the car to accelerate constantly to a stop in exactly 99m? (b) What is the acceleration on the driver? Give your answer in m/s. 25 A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later. (Draw a Velocity Time Graph and list the information) (a) Find how far the car moves while stopping? (b) What is the acceleration of the car? (a) 9.1 s h (b) m/s 2 3, 0844 km/hr 2 (a) 115 m (b) m/s 2 30 A car enters the freeway with a speed of 23 km/h and accelerates to a speed of 86 km/h in 3.5 min. (Draw a Velocity Time Graph and list the information) (a) How far does the car move while accelerating? (b) What is the acceleration? Give your answer in m/s 26 A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. (Draw a Velocity Time Graph and list the information) (a) Find the distance the car travels during this time. (b) What is the acceleration of the car? (a) 3168 m (b).083 m/s km/hr 2 (a) 21 m (b) 1.01 m/s 2 31 A car moving westward 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? (a) +1.6 m/s 2 (b) +24 m/s (c) 240m
4 32 A car accelerates uniformly from rest to a speed of 65 km/h (18 m/s) in 12 s. Find the distance the car travels during this time. 110 m 38 A driver of a car traveling at  15 m/s applies the brakes, causing a uniform acceleration of +2.0 m/s 2. The brakes are applied for 2.5 s. (a) What is the velocity of the car at the end of the braking period? (b) How far has the car moved during the braking period? 33 A dump truck with an average acceleration of 0.80 m/s 2 reaches a velocity of 27 m/s from rest. (Draw a Velocity Time Graph and list the information) (a) How long does it take? (b) How far does it travel when it reaches that velocity? (a) 10 m/s (b) m 39 A ball initially at rest rolls down a hill with an acceleration of 3.3 m/s 2. If it accelerates for 7.5 s, how far will it move? (a) 34 seconds (b) 455 m 34 A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8 m/s 2 for 15 s before takeoff. (a) What is its speed at take off? (b) How long must the runway be for the plane to be able to take off? m A car accelerates from rest at m/s 2 (a) What is the velocity at the end of 5.0 s? (b) What is the displacement after 5.0 s? (a) 72 m/s (b) 540 m (a) 15 m/s (b) 38 m 35 A car with an initial speed of 23.7 km/h accelerates at a uniform rate of 0.92 m/s 2 for 3.6 s. Find the final speed and the displacement of the car during this time. 41 An aircraft has a landing speed of 302 km/h. The landing area of an aircraft carrier is 195 m long. (a) What is the minimum constant acceleration required for a safe landing? (b) How long does it take to come to a stop once it has landed? 36 (a) 36 km/hr 9.9 m/s (b) km m An automobile with an initial speed of 4.30 m/s accelerates at the rate of 3.00 m/s 2. Find the final speed and the displacement after 5.0 s. (a) 19 m/s (b) 59 m 42 Board Problem (a) m/s 2 (b) 4.65 seconds An electron is accelerated from rest in an accelerator at 4.5 x 10 7 m/s 2 over a distance of 95 km. (a) Assuming constant acceleration, what is the final velocity of the electron? (b) What is the time it takes to reach it s final velocity? 37 A car starts from rest and travels for 5.0 s with a uniform acceleration of 1.5 m/s 2. (a) What is the final velocity of the car? (b) How far does the car travel in this time interval? (a) 7.5 m/s (b) 18.8 m 43 (a) 2.92 x 10 6 m/s (b).065 seconds A baby sitter pushing a stroller starts from rest and accelerates at a rate of m/s 2. (a) What is the velocity of the stroller after the stroller has traveled 6.32 m. (b) What is the time it takes to reach the final velocity? (a) m/s (b) 5 seconds
5 44 A car traveling initially at +7.0 m/s accelerates at the rate of m/s 2 for a distance of 245 m. (a) What is its velocity and time at the end of the acceleration? (b) What is its velocity and time after it accelerates for 125 m? (c) What is its velocity and after it accelerates for 67 m? 50 A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s 2. The driver then applies the brakes, causing a uniform acceleration of 2.0 m/s 2. If the brakes are applied for 3.0 s, how fast is the car going at the end of the braking period, and how far has it gone from its start? 45 (a) 21 m/s 17.5 seconds (b) m/s seconds (c) 12.5 m/s 6,8 seconds A gull soaring in a straight line with an initial velocity of 32 m/s accelerates at a rate of +3.0 m/s 2 for 9.0 s. (a) What is the gull's velocity at the end of the acceleration? (b) What is the displacement of the gull at the end of the 9.0 s? m/s 32.3 m A speedboat increases its velocity from 25 m/s to the west to 35 m/s to the west in a distance of 250 m. (a) Find the magnitude of the boat's acceleration. (b) Find the time it takes the boat to travel this distance. (a) 1 m/s 2 to the west (b) 8.3 s 46 (a) 5 m/s (b) m An aircraft has a lift off speed of 120 km/h. (a) What minimum constant acceleration does this require if the aircraft is to be airborne after a takeoff run of 240 m? Give your answer in m/s 2. (b) How long does it take the aircraft to become airborne? 52 A plane lands with a velocity of +120 m/s and accelerates at a maximum rate of 6.0 m/s 2 (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? (b) Can this plane land on a naval aircraft carrier where the runway is 0.80 km long? 47 (a) 2.3 m/s 2 30,000 km/hr 2 (b) 14.4 s Marisa s car accelerates at a rate of m/s 2. (a) How long does it take for Marisa s car to accelerate from a speed of 88.5 km/h to a speed of 96.5 km/h? (b) What is the displacement of Marisa s car? 53 (a) 2.0 x 10 1 s (b) No the plane needs at least 1.2 km to land. A man named Bungkas climbed a palm tree in 1970 and built himself a nest there. In 1994 he was still up there, and he had not left the tree for 24 years. Suppose Bungkas asks a villager for a newspaper, which is thrown to him straight up with an initial speed of 12.0 m/s. When Bungkas catches the newspaper from his nest, the newspaper's velocity is 3.0 m/s, directed upward. From this information, find the height at which the nest was built. Assume that the newspaper is thrown from a height of 1.50 m above the ground. (a) 0.85 s (b) 22,4 n 48 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 before takeoff. (a) What is the plane's velocity at takeoff (b) What is the time required for takeoff? m Nathan accelerates his skateboard along a straight path from rest to 12.5 m/s in 2.5 s (a) What is Nathan s acceleration? (b) What is Nathan s displacement during this time interval? (c) What is Nathan s average velocity during this time interval? (a) 71.6 m/s (b) 44.7 s 49 A bus slows down uniformly from 75.0 km/h (21 m/s) to 0.0 km/h in 220 m. How long does it take to stop? (a) 5.0 m/s 2 (b) 15.6 m (c) 6.25 m/s 21 s
6 55 A baby sitter pushing a stroller starts from rest and accelerates at a rate of m/s 2. (a) What is the velocity of the stroller after it has traveled 4.75 m? (b) How long does it take to reach that velocity? 59 A speeder passes a parked police car at 30.0 m/s. The police car starts from rest with a uniform acceleration of 2.44 m/s 2 (a) How much time passes before the police car overtakes the speeder? (b) How far does the police car get before overtaking the speeder? (c) What is the speed of the police car when he catches the speeder? (a) 2.18 m/s (b) 4.36 seconds Two subway stops are separated by 1100 m. A subway train accelerates at +1.2 m/s 2 from rest through the first half of the distance and decelerates at 1.2 m/s 2 through the second half. (a) What is its travel time? (b) What is its maximum speed? (c) Graph x, v, and a versus t for the trip. (a) 60.6 s; (b) 36.3 m/s A shuffleboard disk is accelerated at a constant rate from rest to a speed of 6.0 m/s over a 1.8 m distance by a player using a cue. At this point the disk loses contact with the cue and slows at a constant rate of 2.5 m/s 2 until it stops. (a) How much time elapses from when the disk begins to accelerate until it stops? (b) What total distance does the disk travel? 60 (a) 24.6 s (b) 738 m (c) m/s A mountain climber stands at the top of a 50.0m cliff hanging over a calm pool of water. The climber throws two stones vertically 1.0 s apart and observes that they cause a single splash when they hit the water. The first stone has an initial velocity of +2.0 m/s. (a) How long after release of the first stone will the two stones hit the water? (b) What is the initial velocity of the second stone when it is thrown? (c) What will the velocity of each stone be at the instant both stones hit the water? (a) 3.40 s (b) 9.2 m/s (c) m/s; 33 m/s 58 Problem (a) 3.0 s; (b) 9.0 m An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at m/s 2. At t 1 the rocket engine is shut down and the sled moves with constant velocity v until t 2. The total distance traveled by the sled is 5.30 x 10 3 m and the total time is 90.0 s. Find t 1, t 2, and v. 61 A professional race car driver buys a car that can accelerate at +5.9 m/s 2. The racer decides to race against another driver in a soupedup stock car. Both start from rest, but the stockcar driver leaves 1.0 s before the driver of the sports car. The stock car moves with a constant acceleration of +3.6 m/s 2 (a) Find the time it takes the sportscar driver to overtake the stockcar driver. (b) Find the distance the two drivers travel before they are side by side. (c) Find the velocities of both cars at the instant they are side by side. 4.6 s 85.3 s +61 m/s (a) 4.6 s after stock car starts (b) 38 m (c) +17 m/s (stock car) +21 m/s (sports car)
7 62 Two cars are traveling along a straight line in the same direction, the lead car at 25 m/s and the other car at 35 m/s. At the moment the cars are 45 m apart, the lead driver applies the brakes, causing the car to have an acceleration of 2.0 m/s 2. (a) How long does it take for the lead car to stop? (b) Assume that the driver of the chasing car applies the brakes at the same time as the driver of the lead car. What must the chasing car's minimum negative acceleration be to avoid hitting the lead car? (c) How long does it take the chasing car to stop? A worker drops a wrench from the top of a tower 80.0m tall. With what velocity does the wrench strike the ground? m/s A gumdrop is released from rest at the top of the Empire State Building, which is 381 m tall. Disregarding air resistance, calculate the displacement and velocity of the gumdrop after 1.00, 2.00, and 3.00 s. 63 (a) 12.5 s (b) 3.1 m/s 2 (c) 11 s A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 950 m apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s 2. Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop. 1 Second m m/s 2 Seconds m m/s 3 Seconds m m/s yes, 0, 10 m/s 69 Jason hits volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0 m above the floor, how long will it be in the air before it strikes the floor? Assume that Jason is the last player to touch the ball before it hits the floor? 64 An astronaut drops a feather from 1.2 m above the surface of the moon. If the acceleration of gravity on the moon is 1.62 m/s 2 down, how long does it take the feather to hit the surface? 1.50 s s A robot probe drops a camera off the rim of a 24kmdeep crater on Mars, where the freefall acceleration is 3.7 m/s 2. (a) Find the time required for the camera to reach the crater floor. (b) Find the velocity with which it hits. 70 Jason hits volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. The volleyball starts from 2.0 m above the floor. (a) Calculate the displacement of the volleyball 0.50 s after Jason hits it. (b) Calculate the velocity of the volleyball 0.50 s after Jason hits it. (a) 1.8 m (b) 1.1 m/s 66 (a) 114 s (b) 421 m/s A pebble is dropped down a well and hits the water 1.5 s later. Using the equations for motion with constant acceleration, determine the distance from the edge of the well to the water's surface. 71 Stephanie serves the volleyball from a height of 0.80 m and gives it an initial velocity of +7.6 m/s straight up. (a) How high will it go? (b) How long will it take the ball to reach its maximum height? (Hint: At maximum height, v = 0 m/s.) 11 m (a) 3.7 m (b) 0.77 s
8 72 A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. (a) What will its speed be when it returns to its starting point? (b) How long will it take for it to reach its starting point? (c) How high does the tennis ball go? 77 A physics student throws softball straight up into the air. The ball was in the air for a total of 3.56 s before it was caught at its original position. (a) What was the initial velocity of the ball? (b) How high did it rise? (a) 8.0 m/s (b) 1.63 s (c) 3.27 m (a) 17.5 m/s (b) 15.5 m 73 Maria throws an apple vertically upward from a height of 1.3 m with an initial velocity of m/s. (a) Will the apple reach Maria's friend in a tree house 5.3 m above the ground? (b) If the apple is not caught, how long will the apple be in the air before it hits the ground? 78 A peregrine falcon dives at a pigeon. The falcon starts downward from rest with freefall acceleration. If the pigeon is 76.0 m below the initial position of the falcon, how long does it take the falcon to reach the pigeon? Assume that the pigeon remains at rest s 74 (a) Yes (b) 2.63 seconds A coin is tossed upward(d) (a) What happens to its velocity while it is in the air? (b) Does its acceleration increase, decrease, or remain constant while it is in the air? 79 A juggler throws a bowling pin into the air with an initial velocity vi. Another juggler drops a pin at the same instant. Compare the accelerations of the two pins while they are in the air. The two pins have the same acceleration (9.81 m/s 2 ) (a) The coin s velocity decreases becomes zero at its maximum height. And then increases in the negative direction until it hits the ground. (b) the coin s acceleration remains constant 80 Kyle is flying a helicopter and it is rising at 5.0 m/s when he releases a bag. After 2.0 s, (a) What is the bag's velocity? (b) How far has the bag fallen? (c) How far below the helicopter is the bag? 75 A ball is thrown vertically upward. What are its velocity and acceleration when it reaches its maximum altitude? What is its acceleration just before it hits the ground? (a) 15 m/s (b) 10 m/s (c) 20 m 76 At maximum altitude, v = 0 and a = m/s 2. Just before the ball hits the ground, a = m/s 2. A ball is thrown vertically upward. (a) What happens to the ball's velocity while the ball is in the air? (b) What is its velocity when it reaches its maximum altitude? (c) What is its acceleration when it reaches its maximum altitude? (d) What is its acceleration just before it hits the ground? (e) Does its acceleration increase, decrease, or remain constant? 81 A model rocket is launched straight upward with an initial speed of 70.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s 2 until its engines stop at an altitude of 250 m. (a) What is the maximum height reached by the rocket? (b) When does the rocket reach maximum height? (c) How long is the rocket in the air? (a) The ball s velocity decreases, becomes zero at its maximum altitude, then increases in the negative direction. (b) At maximum altitude, the ball s velocity is zero. (c) m/s 2 (d) m/s 2 (e) the ball s acceleration remains constant 82 Kyle is flying a helicopter and it is rising at 5.0 m/s when he releases a bag. (a) What hat is the bag's velocity after two seconds (b) How far has the bag fallen after two seconds (c) How far below the helicopter is the bag after two seconds? (a) 15 m/s (b) 10 m/s (c) 20 m
9 83 A flowerpot falls from a windowsill 25.0 m above the sidewalk. (a) How fast is the flowerpot moving when it strikes the ground? (b) How much time does a passerby on the sidewalk below have to move out of the way before the flowerpot hits the ground? 88 A small firstaid kit is dropped by a rock climber who is descending steadily at 1.9 m/s. (a) What is the velocity of the firstaid kit after 2.5 s? (b) How far is the kit below the climber after 2.5 s? 84 (a) m/s (b) 2.25 s Two children are bouncing small rubber balls. One child simply drops a ball. At the same time, the second child throws a ball downward so that it has an initial speed of 10 m/s. What is the acceleration of each ball while in motion? m/s 30.8 m A hotair balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground? m/s 2 (a) 5.4 s; (b) 41 m/s 85 Two students are on a balcony 19.6m above the street. One student throws a ball vertically downward at 14.7 m/s. At the same instant; the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. (a) What is the difference in the time the balls spend in the air? (b) What is the velocity of each ball as it strikes the ground? (c) How far apart are the balls s after they are thrown? 90 A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. (a) In how much time does it pass through the last 20% of its fall? (b) What is its speed when it begins that last 20% of its fall? (c) What is its speed when it reaches the valley beneath the bridge? 86 (a) 3.0 s (b) m/s m/s (c) 23.6 m A small fish is dropped by a pelican that is rising steadily at 0.50 m/s. (a) After 2.5 s, what is the velocity of the fish? (b) How far below the pelican is the fish after 2.5 s? (a) 24 m/s (b) 31 m 91 (a) 0.45 s; (b) 38 m/s; (c) 42 m/s A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. The stones strike the water at the same time. (a) What is the initial speed of the second stone? (b) Plot velocity versus time on a graph for each stone, taking zero time as the instant the first stone is released. 87 A parachutist descending at a speed of 10.0 m/s loses a shoe at an altitude of 50.0 m. (a) When does the shoe reach the ground? (b) What is the velocity of the shoe just before it hits the ground? (c) How high is the parachutist when the show hits the floor (a) 12.3 m/s (b) (a) 2.33 s (b) m/s (c) 26.7 m 92 A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. The stones strike the water at the same time. (a) What is the initial speed of the second stone? (b) Plot velocity versus time on a graph for each stone, taking zero time as the instant the first stone is released. (a) 12.3 m/s
10 93 You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of v 0 = 55 km/h; your best deceleration rate has the magnitude a = 5.18 m/s 2. Your best reaction time to begin braking is T = 0.75 s. (a) To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light is 40 m and 2.8 s? (b) To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light is 32 m and 1.8 s? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works) A ranger in a national park is driving at 56 km/h when a deer jumps onto the road 65 m ahead of the vehicle. After a reaction time of t seconds, the ranger applies the brakes to produce an acceleration of 3.0 m/s 2. What is the maximum reaction time allowed if the ranger is to avoid hitting the deer? 1.57 s One swimmer in a relay race has a 0.50 s lead and is swimming at a constant speed of 4.00 m/s. The swimmer has 50.0 m to swim before reaching the end of the pool. A second swimmer moves in the same direction as the leader. What constant speed must the second swimmer have in order to catch up to the leader at the end of the pool? (a) either; (b) neither 4.17 m/s 94 A test rocket is fired vertically upward from a well. A catapult gives it initial velocity 80.0 m/s at ground level. Its engines then fire and it accelerates upward at 4.00 m/s 2 until it reaches an altitude of 1,000 m. At that point its engines fail and the rocket goes into free fall, with an acceleration of 9.80 m/s 2. (a) How long is the rocket in motion above the ground? (b) What is its maximum altitude? (c) What is its velocity just before it collides with the Earth? 98 An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at m/s 2. At t 1 the rocket engine is shut down and the sled moves with constant velocity v until t 2. The total distance traveled by the sled from start to t 2 is 5300 m and the total time is 90.0 s. At the 5800 in mark, the sled begins to accelerate at 7.0 m/s 2. (a) Find t 1 (b) Find t 2 (c) Find v (d) What is the final position of the sled from the start when it comes to rest? (e) How long does it take for the sled to come to rest from the 5800 mark? 95 The maximum acceleration that is tolerable for passengers in a subway train is 1.34 m/s 2 and subway stations are located 806 m apart. (a) What is the maximum speed a subway train can attain between stations? (b) What is the travel time between stations? (c) If a subway train stops for 20 s at each station, what is the maximum average speed of the train, from one startup to the next? (d) Graph x, v, and a versus t for the interval from one startup to the next. (a) 32.9 m/s; (b) 49.1 s; (c) 11.7 m/s 99 (a) 4.6 s (b) 85 s (c) 60 m/s (d) 6083 m (e) 8.64 s In the figure, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at x 0 = 0 and the green car is at x 0 = 220 m. If the red car has a constant velocity of 20 km/h, the cars pass each other at x = 44.5 m, and if it has a constant velocity of 40 km/h, they pass each other at x = 76.6 m. (a) What is the initial velocity of the green car? (b) What is the acceleration of the green car? (a) 50 km/h; (b) 2.0 m/s 2
11 A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, a ball is dropped from rest from a building 15 m high. After how long will the balls be at the same height? 0.60 s A rocket moves upward, starting from rest with an acceleration of m/s 2 for 4.00 s. It runs out of fuel at the end of the 4.00 s but does not stop. How high does it rise above the ground? 105 A lead ball is dropped in a lake from a diving board 5.20 m above the water. It hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. It reaches the bottom 4.80 s after it is dropped. (a) How deep is the lake? (b) What is the magnitude of the average velocity of the ball for the entire fall? (c) What is the direction (up or down) of the average velocity of the ball for the entire fall? Suppose that all the water is drained from the lake. The ball is now thrown from the diving board so that it again reaches the bottom in 4.80 s. (d) What is the magnitude of the initial velocity of the ball? (e) What is the direction of the initial velocity of the ball? m A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s 2 until its engines stop at an altitude of 150 m. (a) What is the maximum height reached by the rocket? (b) When does the rocket reach maximum height? (c) How long is the rocket in the air? 106 (a) 38.1m; (b) 9.02 m/s; (c) down; (d) 14.5 m/s; (e) up Two diamonds begin a free fall from rest from the same height, 1.0 s apart. How long after the first diamond begins to fall will the two diamonds be 10 m apart? 1.5 s 103 (a) 308 m (b) 8.53 s (c) 16.4 s Water drips from the nozzle of a shower onto the floor 200 cm below. The drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. (a) When the first drop strikes the floor, how far below the nozzle is the second drop? (b) When the first drop strikes the floor, how far below the nozzle is the third drop? 107 A basketball player grabbing a rebound jumps 76.0 cm vertically. (a) How much total time (ascent and descent) does the player spend in the top 15.0 cm of this jump (b) How much total time (ascent and descent) does the player spend in the bottom 15.0 cm? (c) Do your results explain why such players seem to hang in the air at the top of a jump? (a) 350 ms; (b) 82 ms (each includes both ascent and descent through the 15 cm) (a) 89 cm; (b) 22 cm 104 A steel ball is dropped from a building's roof and passes a window, taking s to fall from the top to the bottom of the window, a distance of 1.20 m. It then falls to a sidewalk and bounces back past the window, moving from bottom to top in s. Assume that the upward flight is an exact reverse of the fall. The time the ball spends below the bottom of the window is 2.00 s. How tall is the building? 20.4 m
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