A baseball is thrown at 88 mi/h and with a spin rate of 1500 rev/min. If the distance between the pitcher’s point of release and the catcher’s glove is about 61 feet, estimate how many revolutions the ball makes between release and catch. Neglect any effects of gravity or air resistance on the ball’s flight

Question

A baseball is thrown at 88 mi/h and with a spin rate of 1500 rev/min. If the distance between the pitcher’s point of release and the catcher’s glove is about 61 feet, estimate how many revolutions the ball makes between release and catch. Neglect any effects of gravity or air resistance on the ball’s flight

Answer 1

speed = v = 88 mi/hr * 1 hr/ 3600s * 5280 ft/mi

time = t = 61 ft /v in seconds

turns = 1500 rev/min *1min/60s * t

Answer 2

To estimate the number of revolutions the ball makes between release and catch, we can first convert the speed from miles per hour to feet per minute (since the distance is given in feet).

1 mile = 5280 feet
1 hour = 60 minutes

So, the speed of the ball is:
88 mi/h * 5280 ft/mi * 1/60 h/min = 92.8 ft/min

Next, we can calculate the distance the ball travels in one minute:
92.8 ft/min * 1 min = 92.8 ft

Now, we can find how many times the ball spins in one minute:
1500 revolutions per minute

Finally, we can calculate the number of revolutions the ball makes in the distance between release and catch (61 feet):
61 ft / 92.8 ft/rev = 0.657 revolutions

Therefore, the ball makes approximately 0.657 revolutions between release and catch.

Answer 3

To estimate the number of revolutions the baseball makes between release and catch, we need to convert the given units to a common unit for time.

First, let's convert the speed from miles per hour (mi/h) to feet per minute (ft/min). To do this, we multiply the speed in mi/h by the conversion factor of 5280 ft/mi and divide by 60 min/h:

88 mi/h * (5280 ft/mi / 60 min/h) = 774.4 ft/min

Next, let's convert the spin rate from revolutions per minute (rev/min) to revolutions per second (rev/s). Since there are 60 seconds in a minute, the conversion is as follows:

1500 rev/min * (1 min/60 s) = 25 rev/s

Now that we have both the linear speed and spin rate in consistent units, we can estimate the number of revolutions the baseball makes during the time it travels the given distance.

The time it takes for the ball to travel 61 feet can be calculated using the formula time = distance / speed:

time = 61 ft / 774.4 ft/min = 0.0788 min

Since the spin rate is given in revolutions per second, we need to convert the time from minutes to seconds:

time = 0.0788 min * (60 s/min) = 4.728 s

Now we can estimate the number of revolutions by multiplying the spin rate by the time:

number of revolutions = spin rate * time = 25 rev/s * 4.728 s ≈ 118.2 revolutions

Therefore, we can estimate that the baseball makes approximately 118 revolutions between release and catch.