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 67.2-kg athlete jumps down onto the platform from a height of 0.606 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? Magnitude is 961 N * S Direction is Upwards

(b) With what speed did she reach the platform? 3.44 m/s

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

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

NEED ANSWERS FOR C AND D!!!! Thank You

Explanation / Answer

a) Impulse, for small interval, dI = Fdt = (9200t - 11500t^2)dt
Net impulse, I = [4600t^2 - 3833.33t^3]
applying limits from 0 to 0.8s
I = 981.333 Ns
b) let the speed be v
0.5mv^2 = mgh
v = sqroot(2gh) = 3.446 m/s
c) momentum transferred to the athlete = impulse = 981.333 Ns
final momentum = Initial momentum - Impulse = 67.2*3.446 - 981.333 = -749.735 Ns = mu [ where u is the velocity with whcich the athlete leaves the board]
u = 749.735/67.2 = 11.156 m/s [upward direction]
d) let the hieght be h
0.5(11.156)^2 = 9.8*h
h = 6.3507 m

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