A force platform is a tool used to analyze the performance of athletes measuring

Question

A force platform is a tool used to analyze the performance of athletes measuring the vertical force that the athlete exerts on the ground as a function of time. Starting from rest, a 62.4-kg athlete jumps down onto the platform from a height of 0.636 m. While she is in contact with the platform during the time interval 0 < t < 0.800 s, the force she exerts on it is described by the function F = 9 200t - 11 500t^2 where F is in newtons and t is in seconds.

A)What impulse did the athlete receive from the platform? 981.33 b)With what speed did she reach the platform? 3.53
c)With what speed did she leave it?
d)To what height did she jump upon leaving the platform?

I got part a and b right but not c,d.

Explanation / Answer

impulse = change in momentum as I = integral of F . dT and F = dP/dT so impulse is 981.33 Nsec = mv final - mv initial note F = 9200t 11500t^2 equating F = 0 we get t = 0.8 sec so till t=0.8s, force exerted by athlete is negative, for t>.8 s it is positive due to newton's 3rd law, force exerted by platform is equal and opposite -981.33 = 62.4(v - 3.53) v = -12.16 m/s using work - energy theorem mgh = 1/2mv^2 h = 1/2 * v^2/g = 7.58m

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