A bicycle wheel whose tire radius is 14 inches is rotating at 120 revolutions per minute. How fast is the bicycle moving in feet per second (to the nearest whole number)?

To understand how fast the bicycle is traveling, we first need to determine the distance the wheel covers in a single rotation. This distance is equal to its circumference. With a given radius of 14 inches, the diameter is 28 inches. The circumference is calculated by multiplying the diameter by pi (approximately 3.14159), which gives us about 87.96 inches. This means that for every full turn of the wheel, the bicycle moves forward almost 88 inches. This fundamental relationship between a wheel's size and the distance it travels per revolution is the basis for how odometers calculate the distance a vehicle has traveled.

Next, we factor in the speed of rotation. The wheel is spinning at 120 revolutions per minute, so to find the total distance covered in one minute, we multiply the distance of one rotation (87.96 inches) by 120. This results in a speed of approximately 10,555 inches per minute. To make this large number easier to grasp, we can convert it to feet. Since there are 12 inches in a foot, we divide 10,555 by 12, which tells us the bicycle is moving at about 880 feet per minute.

The final step is to convert this speed from feet per minute to the more familiar feet per second. Because there are 60 seconds in a minute, we divide the speed in feet per minute by 60. So, 880 feet per minute divided by 60 seconds gives us a final speed of approximately 14.66 feet per second. This calculation is a great example of how mathematical principles can be applied to everyday objects to understand their motion and speed.