Question

A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. The cyclist pedals at 175 rpm. Find the linear speed of the bicycle in in/min. How fast is the bike moving in mph?

A) [fill in] in/min, [fill in] mph

B) [fill in] in/min, [fill in] mph

C) [fill in] in/min, [fill in] mph

D) [fill in] in/min, [fill in] mph

Answer 1

The linear speed of the bicycle is 1225π in/min. The bike is moving at a speed of 7.39 mph.

Step-by-step explanation:

To find the linear speed of the bicycle, we can use the formula:

Linear Speed = (Angular Speed) x (radius)

For the front sprocket:

Angular Speed = (175 rpm) x (2π rad/min) = 175π rad/min

Radius = 7 in

Therefore, Linear Speed = (175π rad/min) x (7 in) = 1225π in/min

To find the speed in mph, we need to convert the linear speed from inches per minute to miles per hour:

1 mile = 63,360 inches

1 hour = 60 minutes

Therefore, Linear Speed in mph = (1225π in/min) x (1 mile/63,360 inches) x (60 min/1 hour) = 7.39 mph