Question

The rear wheel of a lawn tractor has a 20-inch radius. Find the angle (in radians) through which a wheel rotates in 23 seconds if the tractor is traveling at a speed of 13 miles per hour? Round to the nearest tenth if necessary.

Answer 1

Answer:

263.12 radians

Step-by-step explanation:

The length of the rear wheel is given by:

$L=2\pi r\\L=40\pi$

The distance traveled by the lawn tractor in 23 seconds is:

$d=13\frac{miles}{hour} *63360\frac{inch}{miles}*\frac{1\ hour}{3600\ seconds}*23\ seconds\\ d=5,262.4\ inches$

The angle through which a wheel rotates is given by:

$A=\frac{d}{L}*2\pi \\A=\frac{5,262.4}{40\pi}*2\pi\\A=263.12\ radians$

The wheel rotates through a 263.12 radians angle.