## Sunday, 3 January 2016

### Measurement and vectors Questions

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
meant?
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
reasoning.
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