Question

A bicyclist races on a bicyclist with 13-inch-radius wheels. When she is traveling at a speed of 37 ft/sec, how many revolutions per minute are her wheels making?

Answer 1

To find the RPM, first calculate the circumference of the wheels using their radius, convert the cyclist's speed into revolutions per second, and then multiply by 60 to convert to RPM. The calculation results in approximately 326.04 RPM.

Step-by-step explanation:

Calculating Wheel Revolutions per Minute

To find out how many revolutions per minute (RPM) the bicyclist’s wheels are making, we need to use the given information that the wheels have a radius of 13 inches and the bicyclist is traveling at a speed of 37 ft/sec. The circumference of the wheel, which is the distance the wheel covers in one revolution, is calculated as:

Circumference = 2 × π × radius

First, we convert the radius of the wheel to feet (1 inch = 1/12 feet):
13 inches × (1/12 feet/inch) = 1.0833 feet

Then we calculate the circumference:
Circumference = 2 × π × 1.0833 feet = 6.8068 feet

Now we can calculate the number of revolutions the wheel makes per second by dividing the bicyclist's speed by the circumference of the wheel:

Revolutions per second = speed / circumference
= 37 ft/sec / 6.8068 feet per revolution = 5.434 revolutions per second

To convert revolutions per second to RPM, we multiply by 60 seconds per minute:

Revolutions per minute = revolutions per second × 60 sec/min
= 5.434 rev/sec × 60 sec/min = 326.04 RPM