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, a57.6-kg athlete jumps down onto the platform from a height of 0.684 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?

N · s?

(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

N · s?

Explanation / Answer

a) Force varies in the time interval from 0 to 0.8 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 0.8
= 981 N-s

b) v = sqrt(2*a*h) = sqrt(2*9.8*0.684) = 3.66 m/s

c) Impulse = Final Momentum - Initial Momentum
vf = (I + mv0)/m = 20.7 m/s

d) h = (20.7)^2 / 19.6 = 21.86 m

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