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Chapter 8: Problem 7

A good baseball pitcher can throw a baseball toward home plate at \(85 \mathrm{mi} / \mathrm{h}\) with a spin of 1800 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 -ft trajectory is a straight line.

Short Answer

Expert verified
The baseball makes approximately 14 revolutions on its way to the home plate.

Step by step solution

01

Convert Speed to Feet per Minute

First we need to convert the speed of the pitch from miles per hour to feet per minute, as the distance is given in feet and the spin in revolutions per minute. We know that 1 mile is equal to 5280 feet and 1 hour is equal to 60 minutes, so \(85 \, \text{mi/hr} = 85 \, \text{mi/hr} \times \frac{5280 \, \text{ft}}{1 \, \text{mi}} \times \frac{1 \, \text{hr}}{60 \, \text{min}} = 7480 \, \text{ft/min}\)
02

Calculate Time

Next, we will find out how long it takes for the baseball to complete the trajectory to the home plate, using the formula for time, which is time = distance / speed. So the time it takes for the baseball to travel 60 feet is \(time = \frac{distance}{speed} = \frac{60 \, \text{ft}}{7480 \, \text{ft/min}} = 0.00802 \, \text{minutes}.\)
03

Calculate Number of Revolutions

Finally, we use the time it takes for the pitch to reach home plate and the rate of spin to calculate how many revolutions the ball makes. We know the baseball is spinning at a rate of 1800 revolutions per minute, so we can use the formula \( \text{revolutions} = \text{rate of spin} \times \text{time} = 1800 \, \text{rev/min} \times 0.00802 \, \text{minutes} = 14.4 \, \text{revolutions}\) thus the baseball makes approximately 14 revolutions on its way to home plate.

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Most popular questions from this chapter

What is the angular speed of a car rounding a circular turn of radius \(110 \mathrm{~m}\) at \(52.4 \mathrm{~km} / \mathrm{h}\) ?

What is the angular speed of \((a)\) the second hand, \((b)\) the minute hand, and \((c)\) the hour hand of a watch?

The flywheel of an engine is rotating at \(25.2 \mathrm{rad} / \mathrm{s}\). When the engine is turned off, the flywheel decelerates at a constant rate and comes to rest after \(19.7 \mathrm{~s}\). Calculate \((a)\) the angular acceleration (in \(\mathrm{rad} / \mathrm{s}^{2}\) ) of the flywheel, (b) the angle (in rad) through which the flywheel rotates in coming to rest, and \((c)\) the number of revolutions made by the flywheel in coming to rest.

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A diver makes \(2.5\) complete revolutions on the way from a 10 -m platform to the water below. Assuming zero initial vertical velocity, calculate the average angular velocity for this drive.
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