Question

the figure shows the chain drive of a bicycle. how far will the bicycle move if the pedals are rotated through 100°? assume the radius of the bicycle wheel is 13.0 inches. the bicycle will travel approximately in. (round to the nearest tenth.)

Explanation:

Step1: Convert degrees to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 100^{\circ}$, then $\theta_{rad}=100\times\frac{\pi}{180}=\frac{5\pi}{9}$ radians.

Step2: Use the arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc - length (distance traveled by the bicycle), $r$ is the radius of the wheel, and $\theta$ is the angle in radians. Given $r = 13.0$ inches and $\theta=\frac{5\pi}{9}$ radians. Then $s=13\times\frac{5\pi}{9}=\frac{65\pi}{9}\approx 22.7$ inches.

Answer:

$22.7$