Question

Question: 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 travelled? (a) 0.50 km (b) 0.80 km (c) 1.0 km (d) 1.5 km (e) 1.8 km

Short answer

Answer:

The distance travelled by the cyclist is. So, option (C) is the correct answer.

Step-by-step solution

Defining the distance formula

The formula to calculate distance is given by$\mathit{S}\mathbf{=}\mathbf{2}\mathit{\pi }\mathit{r}\mathit{N}$

Here Sis the distance travelled, r is the radius andNis the number of revolutions.

Calculating the distance travelled by the cyclist between her apartment and the cafeteria 

We are given: $r=0.500m$and N = 320 .

The formula to calculate the distance is$S=2\pi rN$.

Put the values of r and N in the given distance formula, we get

$$\begin{gathered} S=2\pi \times 0.500\times 320 \\ S=1005.30 \text{m} \\ S=1.00\times {10}^3\text{m} \\ S=1.0 \text{Km} \end{gathered}$$

Therefore, the distance travelled by the cyclist is equal to 1.00 KM.