please show work

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

Answer 1

The answer is C) 1.0 km.

The circumference of the wheel, c is related to its radius, r=0.5 by

c=2*pi*r=2*pi*0.5 m =pi=3.14 m

This means that every time the wheel turns one revolution and the plastic fork clicks, then the bicycle has traveled 3.14 m.

If the fork clicks 320 times, then the bicycle has traveled 320*3.14 m = 1,005 m=1.005 km.