Question

the radii of the sprocket assemblies and the wheel of a bicycle are 4 inches, 2 inches, and 14 inches respectively. if the cyclist is pedaling at a rate of 1 revolution per second, find the speed of the bicycle in feet per second and miles per hour

Answer 1

speed of bicycle =10 miles/h

Step-by-step explanation:

given data

wheel radii front sprocket= 4 inches

wheel radii back sprocket = 2 inches

radii wheel = 14 inches

pedaling rate = 1 revolution per second

to find out

the speed of the bicycle in feet per second and miles per hour

solution

we know angular velocity ω is =
`(\theta )/(t)`

`{\theta}` is angle and t is time

and linear velocity is V =
`(arc length )/(time)`

linear velocity is V =
`(r \theta )/(t)` = rω

and

we know chain is attach top both sprockets

so velocity on front and back sprockets are equal

so rω front sprockets = rω back sprockets

4 inch × 1 rev/s = 2 inch × ω back sprockets

ω back sprockets = 2 rev/s

we can say here back sprockets is connect to back wheel

so

ω back sprockets = ω back wheel

so

velocity of bicycle = rω wheel

velocity of bicycle =14 inches × 2 rev/s

velocity of bicycle =14 inches × 2 (2 π ) rad/s

velocity of bicycle =56 π inches/s =
`(105\pi )/(33)` miles / h

velocity of bicycle =10 miles/h