1. You are writing an adventure novel in which the hero escapes across the border with a billion dollars’ worth of gold
in his suitcase. Could anyone carry that much gold? Would it fit in a suitcase?
2. A cross-country skier skis 1.00 km north and then 2.00 km east on a horizontal snowfield. How far and in what
direction is she fromthe starting point?
3. After an airplane takes off, it travels 10.4 km west, 8.7 km north, and 2.1 km up. How far is it from the takeoff point?
4. How many correct experiments do we need to disprove a theory?How many do we need to prove a theory? Explain.
5. A guidebook describes the rate of climb of a mountain trail as 120 meters per kilometer. How can you express this
as a number with no units?
6. Suppose you are asked to compute the tangent of 5.00 meters.Is this possible? Why or why not?
7. A highway contractor stated that in building a bridge deck he poured 250 yards of concrete. What do you think he
8. What is your height in centimeters? What is your weight in newtons?
9. What physical phenomena (other than a pendulum or cesium clock) could you use to define a time standard?
10. Describe how you could measure the thickness of a sheet of paper with an ordinary ruler.
11. What are the units of volume? Suppose another student tellsyou that a cylinder of radius r and height h has
volume given byr 3h. Explain why this cannot be right.
12 Three archers each fire four arrows at a target. Joe’s fourarrows hit at points 10 cm above, 10 cm below, 10 cm to
the left,and 10 cm to the right of the center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm
from the center, and Flo’s four arrows all hit within 1 cm of the center. The contest judge says that one of the
archers is precise but not accurate,another archer is accurate but not precise, and the third archer is both accurate
and precise. Which description goes with whicharcher? Explain your reasoning.
13. A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the
track from the north side to the south side? When she makes one complete circle around the track? Explain your
14. Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are
required for three vectors to have a vector sum of zero? Explain your reasoning.
15. One sometimes speaks of the “direction of time,” evolving from past to future. Does this mean that time is a vector
quantity?Explain your reasoning.
16. Air traffic controllers give instructions to airline pilots telling them in which direction they are to fly. These
instructions are called “vectors.” If these are the only instructions given, is the name “vector” used correctly? Why
or why not?
17. Can you find a vector quantity that has a magnitude of zero but components that are different from zero? Explain.
Can themagnitude of a vector be less than the magnitude of any of its components? Explain.
18. (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is
the negative of another? Why? Does your answer here contradict what you said in part (a)?
19. How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to
20. How many years older will you be 1.00 gigasecond from now? (Assume a 365-day year.)
21.With a wooden ruler you measure the length of a rectangular piece of sheet metal to be 12 mm. You use micrometer calipers to measure the width of the rectangle and obtain the value 5.98mm. Give your answers to the following questions to the correct number of significant figures. (a) What is the area of the rectangle? (b) What is the ratio of the rectangle’s width to its length? (c) What is the perimeter of the rectangle? (d) What is the difference
between the length and width? (e) What is the ratio of the length to the width?