(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the vertical jump, an athlete starts from a crouch and

jumps upward to reach as high as possible. Even the best athletes

spend little more than 1.00 s in the air (their "hang time"). Treat

the athlete as a particle and let Y(max) be his maximum height above

the floor. To explain why be seems to bang in the air, calculate the

ratio of the time be is above Y(max/2) to the time it takes him to go

from the floor to that height. You may ignore air resistance.

2. Relevant equations

v=v_{0}-gt

delta y = v_{0}t- 1/2 gt^2

3. The attempt at a solution

so I understood it as it need the ratio of t2 to t1 as t2 the time he need to get from y max/2 to y max and t1 the time from the ground to y max/2

since the displacements are cut two half they are equal so

y_{1}=v_{1}t_{1}-1/2 gt_{1}^2

=y_{2}= v_{2}t_{2}- 1/2 gt_{2}^2

where v1 is initial velocity and v2 is velocity at y max/2

v_{2}=v_{1}-gt_{1}

at y max

0=v_{2}-gt_{2}

v_{2}=gt_{2}

v_{1}=g(t_{1}+t_{2})

then back to the original equation I can express it with only t1 and t2 as variables

g(t_{1}+t_{2})t_{1}-1/2 gt_{1}^2=gt_{2}^2 - 1/2 g t_{2}^2

1/2 t_{1}^2-t_{1}t_{2}=1/2 t^{2}_{2}

I dont know how to work this maybe use to get the ratio should I use the quadratic equation for one of them as a variable?

but I think this is wrong I am sure I took a wrong approach and misunderstood the question I just can't see it.

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# Homework Help: Athelete jump dimensional motion

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