Serious hops

Classical Mechanics Level 2

Basketball teams often measure the vertical jumping ability of the athletes they want to employ. While the average professional basketball player has a vertical jump somewhere around 1 m, the highest ever recorded is by Kadour Ziani. Vertical jumps are usually measured in height, but we're going to measure it by the total time in the air. If Kadour Ziani jumped straight up and landed in the same standing position, and his time in the air was 1.14 seconds, how high was his world record jump in meters ?

Details and assumptions

The acceleration of gravity is $-9.8~\mbox{m/s}^2$ .
You may neglect air resistance.

The answer is 1.59.

1 solution

Captain Awesome
Mar 9, 2014

$y_{max} = \boxed{1.59}$ meters.

It was given that $y = 0$ when $t = 1.14$ seconds. From $y = v_it + \frac{1}{2}gt^2$ We have:

$t(v_i + \frac{1}{2}gt) = 0$

Getting $v_i$ :

$v_i + \frac{1}{2}gt = 0$

$\\v_i = -\frac{1}{2}gt$

$v_i = 5.586$ m/s.

By letting $v_f = 0$ , we can get $y_{max}$ :

$v_f^2 = v_i^2 + 2gy_{max}$

$\\y_{max} = \dfrac{-v_i^2}{2g}$

$y_{max} = \boxed{1.59}$ meters.

Serious hops

The answer is 1.59.

1 solution

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