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 63.6-kg athlete jumps down onto the platform from a height of 0.666 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 500t2

where F is in newtons and t is in seconds.

(a) What impulse did the athlete receive from the platform?

(b) With what speed did she reach the platform?
m/s

(c) With what speed did she leave it?
m/s

(d) To what height did she jump upon leaving the platform?
m

Will rate! thank you

Explanation / Answer

(a) Impulse = force * time

I = int (9200 t - 11500 t^2 ) dt   

I = 9200 t^2/2 - 11500 t^3/3 0 ---> 0.8

I = 9200 * 0.8^2/2 -11500 * 0.8^3/3 = 983.29 Ns

direction up

(b) V = sqrt ( 2 g h ) = sqrt ( 2 * 9.8 * 12.19 ) = 15.45 m/s

(c) Impulse = change in momentum

   983.29 = m ( V -u)

983.29 = 63.6 * V

V = 15.46 m/s

d) h = V^2/ 2g = 15.46^2/2*9.8 = 12.19

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