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 58.0 kg athlete jumps down onto the platform from a height of 0.680 m. While she is in contact with the platform during the time interval 0 < t < 0.8 s, the force she exerts on it is described by the function below. F = (9 200 N/s)t - (11 500 N/s2)t2 Assume the positive y-axis points upward.

(a) What was the athlete's velocity when she reached the platform? Correct: Your answer is correct. -3.653 m/s j hat

(b) What impulse did the athlete receive from the platform? Correct: Your answer is correct. 981.335 Ns j hat

(c) What impulse did the athlete receive from gravity while in contact with the platform? j hat

(d) With what velocity did she leave the platform? j hat

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

Explanation / Answer

I'm with you up through (b)

c) What impulse did the athlete receive from gravity while in contact with the platform?

F = m(g) = 58 (-9.8) = -568.4 N Ft = F (h) = -568.4 (0.8) = -454.72Ns

d)Now gravity has just added an impulse in the downward direction and the platform has added an impulse in the upward direction. The net impulse is

Ft = 981.35 -454.72
Ft = 526.63 Ns upward

and an impulse will equal a change in momentum

Ft = mv
Ft = m(vf - vi)
Ft / m = vf - vi
(Ft / m) + vi = vf

vf = (526.63 /58) - 3.653

vf = 5.426 m/s (upward)

which will be her initial leaving speed

d) my guess is that you will already have the knowledge of this solution.

h = (vf)²/2g =1.5m

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