1. Two children are playing on two trampolines. The first child can bounce up one-and-a-half times
higher than the second child. The initial speed up of the second child is 5.0 m s. (a) Find the
maximum height the second child reaches. (b) What is the initial speed of the first child? (c) How
long was the first child in the air?
2. Consider the street pattern shown in Fig. 2–42. Each intersection has a traffic signal, and the
speed limit is 50 km h. Suppose you are driving from the west at the speed limit. When you are
10 m from the first intersection, all the lights turn green. The lights are green for 13 s each. (a)
Calculate the time needed to reach the third stoplight. Can you make it through all three lights
without stopping? (b) Another car was stopped at the first light when all the lights turned green. It
can accelerate at the rate of 2.0 m s 2 to the speed limit. Can the second car make it through all
three lights without stopping?
3. Every year the Earth travels about 109 km as it orbits the Sun. What is Earth’s average speed in km/h?
4. In coming to a stop, a car leaves skid marks 92 m long on the highway. Assuming a deceleration of
7.00 m s 2 , estimate the speed of the car just before braking.
5. An object starts from rest and falls under the influence of gravity. Draw graphs of (a) its speed and (b)
the distance it has fallen, as a function of time from t 0 to t 5.00 s. Ignore air resistance.
6. Graphically determine the resultant of the following three vector displacements: (1) 34 m, 25º north of
east; (2) 48 m, 33º east of north; and (3) 22 m, 56º west of south. 7. Vector V1 is 6.6 units long and points along the negative x axis. Vector V2 is 8.5 units long and points
at 45º to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum V1 V2 (magnitude and angle).
8. An airplane is traveling 735 km h in a direction 41.5º west of north (Fig. 3–31). (a) Find the components
of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has
the plane traveled after 3.00 h?
9. Three vectors are shown in Fig. 3–32. Their magnitudes are given in arbitrary units. Determine the sum
of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the x
axis.
10. Huck Finn walks at a speed of 0.60 m s across his raft (that is, he walks perpendicular to the raft’s
motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.70 m s
relative to the river bank . What is Huck’s velocity (speed and direction) relative to the river bank?
11. A boat can travel 2.30 m s in still water. (a) If the boat points its prow directly across a stream whose
current is 1.20 m s, what is the velocity (magnitude and direction) of the boat relative to the shore?
(b) What will be the position of the boat, relative to its point of origin, after 3.00 s?
12. Two planes approach each other head-on. Each has a speed of 785 km h, and they spot each other
when they are initially 11.0 km apart. How much time do the pilots have to take evasive action?
13. A 20.0-kg box rests on a table. (a) What is the weight of the box and the normal force acting on it? (b)
A 10.0-kg box is placed on top of the 20.0-kg box. Determine the normal force that the table exerts on the 20.0-kg box and the normal force that the 20.0-kg box exerts on the 10.0-kg box.
14. What average force is required to stop an 1100-kg car in 8.0 s if the car is traveling at 95 km h ?
15. A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the
scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator,
and find the direction of acceleration.
16. Three blocks on a frictionless horizontal surface are in contact with each other, as shown in Fig. 4–51.
A force F is applied to block 1 mass m1 . (a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of m1, m2 , and m3 ), (c) the net force on each block, and
(d) the force of contact that each block exerts on its neighbor. (e) If m1 m2 m3 12.0 kg and
F 96.0 N, give numerical answers to (b), (c), and (d). Do your answers make sense intuitively?
17. A force of 48.0 N is required to start a 5.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 48.0-N force continues, the box accelerates at 0.70 m s 2 . What is the coefficient of kinetic friction?
18. The coefficient of static friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? 19. A car can decelerate at 4.80 m s 2 without skidding when coming to rest on a level road. What would
its deceleration be if the road were inclined at 13º uphill? Assume the same static friction coefficient.
20. (a) A box sits at rest on a rough 30º inclined plane. Draw the free-body diagram, showing all the forces
acting on the box. (b) How would the diagram change if the box were sliding down the plane? (c)
How would it change if the box were sliding up the plane after an initial shove?
21. A 75.0-kg person stands on a scale in an elevator. What does the scale read (in N and in kg) when the elevator is (a) at rest, (b) ascending at a constant speed of 3.0 m s , (c) falling at 3.0 m s , (d) accelerating upward at 3.0 m s 2 , (e) accelerating downward at 3.0 m s 2 ?
22. How much work is done by the gravitational force when a 265-kg pile driver falls 2.80 m? 23. A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is required?
24. A 1300-N crate rests on the floor. How much work is required to move it at constant speed (a) 4.0 m
along the floor against a friction force of 230 N, and (b) 4.0 m vertically?
25. The force on an object, acting along the x axis, varies as shown in Fig. 6–37. Determine the work done
by this force to move the object (a) from x 0.0 to x 10.0 m, and (b) from x 0.0 to x 15.0 m.
26. A spring has k 88 N m. Use a graph to determine the work needed to stretch it from x 3.8 cm to
x 5.8 cm, where x is the displacement from its unstretched length.
27. An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on the arrow over a
distance of 78 cm. What is the speed of the arrow as it leaves the bow?
28. At an accident scene on a level road, investigators measure a car’s skid mark to be 88 m long. The
accident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use
these data to determine the speed of the car when the driver slammed on (and locked) the brakes.
(Why does the car’s mass not matter?)
29. A 1200-kg car rolling on a horizontal surface has speed v 65 km h when it strikes a horizontal coiled
spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
30. A spring with k 53 N m hangs vertically next to a ruler. The end of the spring is next to the 15-cm
mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the
spring line up with the ruler marks?
31. A novice skier, starting from rest, slides down a frictionless 35.0º incline whose vertical height is 185 m.
How fast is she going when she reaches the bottom?
32. In the high jump, Fran’s kinetic energy is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass
2.10 m and cross the bar with a speed of 0.70 m s ?
33. The roller-coaster car shown in Fig. 6–41 is dragged up to point 1 where it is released from rest.
Assuming no friction, calculate the speed at points 2, 3, and 4.
34. A 110-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate? 35. A 21.7-kg child descends a slide 3.5 m high and reaches the bottom with a speed of 2.2 m s. How
much thermal energy due to friction was generated in this process?
36. A 1400-kg sports car accelerates from rest to 95 km h in 7.4 s. What is the average power delivered by
the engine?
37. How much work can a 3.0-hp motor do in 1.0 h?
38. A 95-kg halfback moving at 4.1 m s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5 m s in the same direction, what was their mutual speed immediately after the tackle?
39. A 9300-kg boxcar traveling at 15.0 m s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m s. What is the mass of the second car? 40.A 0.145-kg baseball pitched at 39.0 m s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m s. If the contact time between bat and ball is 3.00103 s, calculate the average force between the ball and bat during contact. 41.A 12-kg hammer strikes a nail at a velocity of 8.5 m s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (b) What is the average force acting on the nail?
42. A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m s. How far apart are
the wave crests (compressions)?
43. (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a
speed of 3.00108 m s. What are the wavelengths of these signals? (b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?
44. A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave
reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point? ( v =
1560m/s)
45. (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz
to 20,000 Hz. (b) What is the wavelength of a 10-MHz ultrasonic wave?
46. An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine
backfire occurs on another boat 1.0 km away. How much time elapses before the backfire is heard (a)
by the fish, and (b) by the fishermen?
47. How many beats will be heard if two identical flutes each try to play middle C (262 Hz), but one is at
5.0°C and the other at 25.0°C?
49. The speed of light in ice is 2.29 108 m s. What is the index of refraction of ice?
50. A dentist wants a small mirror that, when 2.20 cm from a tooth, will produce a 4.5 upright image. What kind of mirror must be used and what must its radius of curvature be? 51. A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature? 52. An aquarium filled with water has flat glass sides whose index of refraction is 1.52. A beam of light
from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular. What is the angle of
this light ray when it enters (a) the glass, and then (b) the water? (c) What would be the refracted
angle if the ray entered the water directly?
53. Light is incident on an equilateral glass prism at a 45.0° angle to one face, Fig. 23–51. Calculate the
angle at which light emerges from the opposite face. Assume that n 1.58.
54. A flashlight beam strikes the surface of a pane of glass (n 1.58) at a 63° angle to the normal. What is
the angle of refraction? 55. The magnification of a convex mirror is 0.65 for objects 2.2 m from the mirror. What is the focal
length of this mirror?
56. A certain lens focuses light from an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual? 57. A stamp collector uses a converging lens with focal length 24 cm to view a stamp 18 cm in front of the lens. (a) Where is the image located? (b) What is the magnification? 58. How far from a converging lens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object? 59. (a) How far from a 50.0-mm-focal-length lens must an object be placed if its image is to be magnified
2.00 and be real? (b) What if the image is to be virtual and magnified 2.00 ?
60. We wish to determine the depth of a swimming pool filled with water. We measure the width
(x 5.50 m) and then note that the bottom edge of the pool is just visible at an angle of 14.0° above
the horizontal as shown in Fig. 23–54. Calculate the depth of the pool.