Chapter 2/3 Problem Set 6. The position versus time for a certain particle moving along the x axis is shown in Figure P2.6. Find the average velocity in the time intervals (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, (e) 0 to 8.00 s. 15. The position versus time for a certain particle moving along the x axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t = 1.00 s, (b) t = 3.00 s, (c) t = 4.50 s, and (d) t = 7.50 s. 19. A particle is moving with a velocity of 60.0 m/s in the positive x direction at t = 0. Between t = 0 and t = 15.0 s the velocity decreases uniformly to zero. What was the acceleration during this 15.0-­‐s interval? What is the significance of the sign of your answer? 22. The velocity-­‐time graph for an object moving along a straight path is shown in Figure P2.22. (a) Find the aver-­‐age accelerations of this object during the time intervals 0 to 5.0 s, 5.0 s to 15 s, and 0 to 20 s. (b) Find the instantaneous accelerations at 2.0 s, 10 s, and 18 s. 26. A truck covers 40.0 m in 8.50 s while smoothly slowing down to final speed 2.80 m/s. (a) Find its original speed. (b) Find its acceleration. 29. A Cessna 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? (b) How long does it take the aircraft to become airborne? 30. A truck on a straight road starts from rest and accelerates at 2.0 m/s2 until it reaches a speed of 20 m/s. Then the truck travels for 20 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.0 s. (a) How long is the truck in motion? (b) What is the average velocity of the truck for the motion described? 32. A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of –5.00 m/s2 as it comes to rest. (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 small tropical island airport where the runway is 0.800 km long? 37. A car starts from rest and travels for 5.0 s with a uniform acceleration of + 1.5 m/s2. The driver then applies the brakes, causing a uniform acceleration of -­‐
2.0 m/s2. If the brakes are applied for 3.0 s, (a) how fast is the car going at the end of the braking period, and (b) how far has it gone? 43. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does it take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started? 45. Killer whales at Sea World routinely jump 7.5 m above the water. What is their speed as they leave the water to achieve this? 46. A peregrine falcon dives at a pigeon. The falcon starts downward from rest and falls with free-­‐fall 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. 47. A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s? 49. 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/s2 until its engines stop at an altitude of 150 m. (a) What is the maximum height reached by the rocket? (b) How long after lift-­‐off does the rocket reach its maximum height? (c) How long is the rocket in the air? 50. A parachutist with a camera, both descending at a speed of 10 m/s, releases that camera at an altitude of 50 m. (a) How long does it take the camera to reach the ground? (b) What is the velocity of the camera just before it hits the ground? Chapter 3
1. A dog searching for a bone walks 3.50 m south, then 8.20 m at an angle 30.0° north of east, and finally 15.0 m west. Find the dog’s resultant displacement vector, using graphical techniques. 9. A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 6.00 m east, and the second, 5.40 m south. What displacement would have been needed to get the ball into the hole on the first putt? 12. While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 125 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance. 15. The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 60.0° north of west with a speed of 41.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island? Figure 3.17 17. A commuter airplane starts from an airport and takes the route shown in Figure P3.17. It first flies to city A located at 175 km in a direction 30.0° north of east. Next, it flies 150 km 20.0° west of north to city B. Finally, it flies 190 km due west to city C. Find the location of city C relative to the location of the starting point. 16. A small map shows Atlanta to be 730 miles in a direction of 5.0° north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21° west of north from Atlanta. Assume a flat Earth and use this information to find the displacement from Dallas to Chicago. 20. An airplane starting from airport A flies 300 km east, then 350 km at 30.0° west of north, and then 150 km north to arrive finally at airport B. (a) The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight? (b) How far will the pilot travel in this direct flight? Assume there is no wind during these flights. 24. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach, as shown in Figure P3.24. How long after being released does the stone strike the beach below the cliff? With what speed and angle of impact does it land? 26. Tom the cat is chasing Jerry the mouse across a table surface 1.5 m above the floor. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 5.0 m/s. Where will Tom strike the floor, and what velocity components will he have just before he hits? What is Tom’s final speed just before hitting the floor? 28. An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point? 29. A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building? 31. A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s2 for a distance of 50.0 m to the edge of the cliff. The cliff is 30.0 m above the ocean. Find (a) the car’s position relative to the base of the cliff when the car lands in the ocean, and (b) the length of time the car is in the air.