Bob has just finished climbing a sheer cliff above a beach and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is ?0=86.0 mph.v0=86.0 mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory) and watches carefully. The ball rises and then falls, and after ?1=0.710 s,t1=0.710 s, the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball landed a distance of ?=354 ftx=354 ft from the base of the cliff. How high up is Bob if the ball started from exactly 5 ft above the edge of the cliff?

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Asked Sep 8, 2019
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Bob has just finished climbing a sheer cliff above a beach and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is ?0=86.0 mph.v0=86.0 mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory) and watches carefully. The ball rises and then falls, and after ?1=0.710 s,t1=0.710 s, the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball landed a distance of ?=354 ftx=354 ft from the base of the cliff. How high up is Bob if the ball started from exactly 5 ft above the edge of the cliff?

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Expert Answer

Step 1

The expression for time of flight

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2v; sin 0

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Step 2

Substituting the values to find θ

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2(86.0 mph) 0.447m/s sin 1mph (0.710 s) (9.8 m/s e=sin (0.0905) =5.19°

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Step 3

The expression for time of flight ...

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R t= 2 cos

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