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11. There is a runner on third with one out. The batter flies out to the center

ID: 1882866 • Letter: 1

Question

11. There is a runner on third with one out. The batter flies out to the center fielder 250.Oft from home plate. The runner tags up and tries to score. The runner takes 1.0s to accelerate at a constant rate to a maximum speed of 24.0ft/s and runs home the rest of the way at this speed. The outfielder takes 1.0s to throw the ball with an average velocity of 80.0ft/s. The throw is right on target and thus the catcher requires no time to apply the tag. Does the runner score? [Note: there are 90ft between the bases in Major League Baseball.]

Explanation / Answer

We need to find the time of reaching home for both (runner and ball)

Runner

t = t1+t2

t1 = time to accelerate = 1 sec

t2 = time to cover rest of the distance

Total distance was 90ft, but he covered a little during acceleration

v = u + at
24 = 0 + ax1
a = 24 ft/s^2

s = ut + 1/2 at^2 = 0 + 1/2 x 24 x 1^2 = 12 ft

rest 90-12 = 78ft is covered at 24ft/s
t2 = dist / speed = 78/24 = 3.25 sec

t = 4.25 sec

Ball

t = t1 + t2

t1 time taken = 1s
t2 = time for ball to reach base = dist/speed = 250 / 80 = 3.125

t = 4.125 s

As ball time is less, it reaches first. Hence, runner is out and doesn't score.

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