Question

question 26. the tires on a car have a diameter of 27 inches. the car runs over a pebble, which sticks inside the tread of one of the tires. if the pebble on the tire rotates at a speed of 9 revolutions per second, find the speed of the car in miles per hour.
a) 43.38
b) 0.72
c) 73.20
d) 4.82
e) 13.20

Explanation:

Step1: Find the circumference of the tire

The formula for the circumference of a circle is $C = \pi d$. Given $d = 27$ inches, so $C=\pi\times27\approx 3.14\times27 = 84.78$ inches.

Step2: Find the distance traveled per second

The tire rotates at 9 revolutions per second. The distance traveled per second $s_1$ is the number of revolutions per second times the circumference. So $s_1=9\times C=9\times84.78 = 763.02$ inches per second.

Step3: Convert inches per second to miles per hour

There are 12 inches in a foot, 5280 feet in a mile, and 3600 seconds in an hour.
First, convert inches per second to feet per second: $s_2=\frac{763.02}{12}=63.585$ feet per second.
Then convert feet per second to miles per hour: $s=\frac{63.585\times3600}{5280}\approx 43.38$ miles per hour.

Answer:

a) 43.38