A Major League fastball is thrown at 92.1 mph and with a spin rate of 103 rpm. If the distance between the pitcher's point of release and the catcher's glove is exactly 61.4 ft, how many full turns does the ball make between release and catch? Neglect any effect of gravity or air resistance on the ball's flight.

Question

A Major League fastball is thrown at 92.1 mph and with a spin rate of 103 rpm. If the distance between the pitcher's point of release and the catcher's glove is exactly 61.4 ft, how many full turns does the ball make between release and catch? Neglect any effect of gravity or air resistance on the ball's flight.

Answer 1

To determine the number of full turns the ball makes between release and catch, we need to consider the relationship between the ball's linear speed, spin rate, and the distance traveled.

First, let's convert the speed from mph to feet per second (fps). Since there are 5280 feet in a mile and 3600 seconds in an hour, we can calculate the conversion factor:

Speed (fps) = (Speed (mph) * 5280 ft/mi) / 3600 s/hr

Plugging in the value:
Speed (fps) = (92.1 mph * 5280 ft/mi) / 3600 s/hr = 134.8 fps (rounded to one decimal place)

Next, let's calculate the linear distance traveled by the ball. Given that the distance between the pitcher's release point and the catcher's glove is 61.4 ft, we will use this value.

Now, we need to calculate the time it takes for the ball to travel this distance:

Time (s) = Distance (ft) / Speed (fps)
Time (s) = 61.4 ft / 134.8 fps

Calculating the time:
Time (s) = 0.455 s (rounded to three decimal places)

Lastly, we need to determine the number of complete revolutions the ball makes within this time. This can be determined by considering the relationship between the spin rate and the time of flight.

Since we know the spin rate is given in revolutions per minute (rpm), we need to convert it to revolutions per second (rps):

Spin rate (rps) = Spin rate (rpm) / 60 s/min
Spin rate (rps) = 103 rpm / 60 s/min = 1.717 rps (rounded to three decimal places)

Now, we can determine the number of complete revolutions made by the ball:

Number of revolutions = Spin rate (rps) * Time (s)
Number of revolutions = 1.717 rps * 0.455 s

Calculating the number of revolutions:
Number of revolutions = 0.782 (rounded to three decimal places)

Therefore, the ball makes approximately 0.782 full turns between release and catch.