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 64.8-kg athlete jumps down onto the platform from a height of 0.594 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 N · s direction

(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

Explanation / Answer

a) Force varies in the time interval from 0 to .8 s. Find the area under the curve of force vs time

Impulse = Force x Time

? (9200t - 11,500t^2) dt. Evaluated it from 0 to .8
= 981 N-s

b) v = sqrt(2*a*h) = sqrt(2*9.8*.594) = 3.41 m/s

c) Impulse = Final Momentum - Initial Momentum
vf = (I + mv0)/m = 18.55 m/s

d) h = (18.55)^2 / 19.6 = 17.56 m

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