A basketball player grabbing a rebound jumps 74 cm vertically. (a) How much (tot

Question

A basketball player grabbing a rebound jumps 74 cm vertically.

(a) How much (total) time does the player spend in the top 25 cm of this jump?
   ms

(b) How much (total) time does the player spend in the bottom 25 cm of this jump?
ms
(c) Does this help explain why such players seem to hang in the air at the tops of their jumps?

No, it is an optical illusion and they spend the same amount of time at the tops and bottoms of their jumps.

No, it is an optical illusion and they spend less time at the tops of their jumps.

Yes, they spend more time at the tops of their jumps.

Explanation / Answer

a) we can answer the first part of this by recognizing the player rises 0.74 m, reaches the apex of motion, and then falls back to the ground

we can ask how long it takes to fall 0.25 m from rest:

dist = 1/2 gt^2 or t=sqrt[2d/g]
t=0.22 s

this is the time to fall from the top; it would take the same time to travel upward the final 0.25 m, so the total time spent in the upper 0.25 m is

2x0.22 = 0.44s

b) there are a couple of ways of finding the time it takes to travel the bottom 0.25m

first way:

we can use

d=1/2gt^2 twice to solve this problem

the time it takes to fall the final 0.25 m is:

time it takes to fall 0.74 m - time it takes to fall 0.49 m

t = sqrt[2d/g] = 0.388 s to fall 0.74 m, and

this equation yields it takes 0.316 s to fall 0.49 m, so it takes 0.072 s to fall the final 0.25 m. The total time spent in the lower 0.25 m is then twice this, or 0.144s

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