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Question

 A rock got stuck in the tread of my tire and when I was driving 70 miles per hour, the rock came loose and hit the inside of the wheel well of the car. How fast, in miles per hour, was the rock traveling when it came out of the tread? (The tire has a diameter of 23 inches.)

Answer 1

The answer is 70 mph, and here is why.

You have to realize that the center of the wheel is also travelling at 70 mph. When the tire makes one complete revolution, the center of the tire travels the same distance as the circumference in the same period of time, so a point on the circumference (the rock) must be travelling at the same rate of speed as the center of the tire which is the same speed as the car. When the rock comes loose, it is travelling tangentially to the circumference at the speed of the car.

You can verify this by taking a circular object, marking a mark on the circumference, making one revolution, and noting the distance the center travelled.

Answer 2

The linear speed has already been given: 70 mph.

This is the value that the rock will travel when it comes out of the tread. Any other information is irrelevant.