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Chapter 2: Problem 24

New York Yankees pitcher Roger Clemens threw a fastball at a horizontal speed of \(160 \mathrm{~km} / \mathrm{h}\), as verified by a radar gun. How long did it take for the ball to reach home plate, which is \(18.4 \mathrm{~m}\) away?

Short Answer

Expert verified
The ball took approximately \(0.414 \mathrm{~s}\) to reach the home plate.

Step by step solution

01

Convert Speed into Correct Units

First, the speed is given in km/h but the distance is presented in meters. In order to use the formula, speed and distance should be in the same unit. Therefore, convert the speed from km/h to m/s by using the conversion factor \(1 \mathrm{~km} / \mathrm{h} = 1000 \mathrm{~m} / 3600 \mathrm{~s}\). So the speed in m/s becomes \(160 \times 1000 / 3600 = 44.44 \mathrm{~m/s}\)
02

Calculate Time

Now using the formula \(time = distance / speed\), we can calculate the time it took for the ball to reach the home plate. Substituting the values we have, \(time = 18.4 \mathrm{~m} / 44.44 \mathrm{~m/s} = 0.414 \mathrm{~s}\)
03

Interpret the Result

The calculated time refers to how long it took for the ball to travel from the pitcher's hand to the home plate. This calculation assumes that the speed of the ball didn't change during the flight, which is an idealization.

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Most popular questions from this chapter

A particle had a velocity of \(18 \mathrm{~m} / \mathrm{s}\) in the \(+x\) direction and 2.4 s later its velocity was \(30 \mathrm{~m} / \mathrm{s}\) in the opposite direction. What was the average acceleration of the particle during this 2.4-s interval?

A car is driven east for a distance of \(54 \mathrm{~km}\), then north for \(32 \mathrm{~km}\), and then in a direction \(28^{\circ}\) east of north for \(27 \mathrm{~km}\). Draw the vector diagram and determine the total displacement of the car from its starting point.

A muon (an elementary particle) is shot with initial speed \(5.20 \times 10^{6} \mathrm{~m} / \mathrm{s}\) into a region where an electric field produces an acceleration of \(1.30 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}\) directed opposite to the initial velocity. How far does the muon travel before coming to rest?

A plane flies \(410 \mathrm{mi}\) east from city \(A\) to city \(B\) in \(45 \mathrm{~min}\) and then \(820 \mathrm{mi}\) south from city \(B\) to city \(C\) in 1 h \(30 \mathrm{~min}\). (a) What are the magnitude and direction of the displacement vector that represents the total trip? What are \((b)\) the average velocity vector and \((c)\) the average speed for the trip?

Maurice Greene once ran the \(100-\mathrm{m}\) dash in \(9.81 \mathrm{~s}\) (the wind was at his back), and Khalid Khannouchi ran the marathon (26 mi, 385 yd) in 2:05:42. (a) What are their average speeds? (b) If Maurice Greene could maintain his sprint speed during a marathon, how long would it take him to finish?
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