problem solving

Question

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.

Answer 1

v = ωr where omega is angular velocity and r is radius.

 

what is omega? 9 rpm = 9(2•pi) radians/sec = 

ω = 56.5487172 rad/(1/3600 hr) = 203575.38 radians/hour

 

Then r is 27" = 2.25 ft = 2.25/5280 mi = 0.000426136 miles

 

Therefore v = ωr = 203,575.38 times .000426136 = 86.75 mi/hr.

 

I LEAVE YOU TO CHECK THIS WORK!