1. Two rectangular rugs are on display in a showroom. If one rug is twice as long as the other, does this necessarily mean that its area is also twice as large as that of the second? Explain.

2. A pendulum clock is taken to a repair shop. Its pendulum is replaced by a shorter one that oscillates with a smaller period than the original. What effect, if any, does this have on how the clock runs?

3. A wind is blowing from the north (the air is moving toward the south). When a person is walking toward the north, is the relative speed of the wind that the person senses greater than, the same as, or less than the speed the person senses when not walking? How about when the person is walking toward the south?

4. List the physical quantities identified in this chapter. From which of the fundamental physical quantities is each derived? Which of them are vectors, and which are scalars?

5. A ball thrown at a brick wall bounces directly back with the same speed it had when it struck the wall. Has the velocity of the ball changed? Explain.

6. Can the resultant of two velocities have zero magnitude? If so, give an example.

7. A basketball player shoots a free throw. Make a sketch showing the basketball's velocity just after the ball leaves the player's hands. Draw in two components of this velocity, one horizontal and one vertical. Repeat the sketch for the instant just before the ball reaches the basket. What is different?

8. As a stop light changes from red to green, a car starts to cross through the intersection. An instant before it begins to move, its velocity is zero. Must its acceleration at that time also be zero. Why or why not? Explain.

9. Using concepts and physical quantities discussed in this chapter, explain why it is usually safe for a person standing on the seat of a chair to jump horizontally and land on the floor, but not for a person standing on the roof of a tall building to jump horizontally and land on the ground.

10. During 200-meter and 400-meter races, runners must stay in lanes as they go around a curved part of the track. If runners in two different lanes have exactly the same speed, will they also have exactly the same centripetal acceleration as they go around a curve? Explain.

11. The following are speeds and headings displayed on a GPS receiver. (Heading gives the direction of motion based on north 5 0, east 5 90, south 5 180, etc.) In each case, indicate whether the receiver was accelerating during the time between the displays and, if it was, describe in what way the receiver was accelerating.

(a) Initially: 60 mph, 70; 5 seconds later: 50 mph, 70.

(b) Initially: 50 mph, 70; 5 seconds later: 70 mph, 70.

(c) Initially: 60 mph, 70; 5 seconds later: 60 mph, 90.

12. If a ball is thrown straight up into the air, what is its acceleration as it moves upward? What is its acceleration when it reaches its highest point and is stopped at an instant?

13. Sketch a graph of velocity versus time for the motion illustrated in Figure 1.24. Indicate what the car's acceleration is at different times.

14. Eight arrows are successively shot straight up into the air. All the arrows have the same size and shape, but are made of different materials and so have different masses (M). The arrows also have different upward speeds (V) as they leave the bow. The data for the eight arrows is shown here. Ignoring any effects associated with air resistance, rank the arrows according to the maximum height that each achieves from greatest to smallest.

Arrow A: M 5 0.075 kg; V 5 16 m/s

Arrow B: M 5 0.180 kg; V 5 12 m/s

Arrow C: M 5 0.100 kg; V 5 18 m/s

Arrow D: M 5 0.075 kg; V 5 12 m/s

Arrow E: M 5 0.120 kg; V 5 10 m/s

Arrow F: M 5 0.090 kg; V 5 16 m/s

Arrow G: M 5 0.180 kg; V 5 10 m/s

Arrow H: M 5 0.050 kg; V 5 8 m/s