Question

A lawnmower has a blade that extends out 1 foot from its center. The tip of the blade is traveling at the speed of sound, which is 1,100 feet per second. Through how many revolutions per minute is the blade turning?

Answer 1

The lawnmower blade is turning at approximately 10,471 revolutions per minute.

Step-by-step explanation:

To find the number of revolutions per minute the lawnmower blade is turning, we need to calculate the speed of the tip of the blade. The speed of sound is 1,100 feet per second, and the blade extends out 1 foot from the center. Since the tip of the blade is traveling at the speed of sound, which is 1,100 feet per second, we can calculate the number of revolutions per second by dividing the speed of sound by the circumference of the blade:

Revolutions per second = Speed of sound / Circumference

Circumference = 2 * π * Radius = 2 * π * 1 = 2π feet

Revolutions per second = 1,100 feet per second / (2π feet) ≈ 174.53 revolutions per second

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

Revolutions per minute = 174.53 revolutions per second * 60 ≈ 10,471 revolutions per minute.