Chapter 10, Problem 1OQ

A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. A piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 0.80 km (c) 1.0 km (d) 1.5 km (e) 1.8 km

To determine

The total distance travelled by the cyclist.

Answer to Problem 1OQ

Option (c).

Explanation of Solution

Write the expression to calculate the distance travelled by the cyclist.

  $S=r\theta$

Here, S is the total distance travelled, $\theta$ is the number of revolutions and r is the wheel radius.

Conclusion:

Substitute $0.500\text{m}$ for r and $320\text{rev}$ for $\theta$ in the above equation to calculate S.

  $\begin{array}{c}S=\left(0.500\text{m}\right)\left(320\text{rev}\right)\left(\frac{2\pi \text{rad}}{1\text{rev}}\right)\\ =1.00\times {10}^3\text{m}\left(\frac{1\text{km}}{{10}^3\text{m}}\right)\\ \text{=1}\text{.0}\text{km}\end{array}$

Thus, the total distance travelled is $\text{1}\text{.0}\text{km}$ and hence option (c) is correct.