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 59.0-kg athlete jumps down onto the platform from a height of 0.590 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 500t^2 where F is in newtons and t is in seconds. (a) What impulse did the athlete receive from the platform? _____________N

Explanation / Answer

F = dP/dt = 9200N/s t - 11500 N/s^2 t^2 so dP = Fdt = 9200N/s^2 t - 11500n/s^2 t^2 Integrating wrt t on the boundaries of 0 s to 0.8s will give the impulse she gives the table (N3 says this is equal in magnitude and opposite in direction to the impulse the table gives her) integrating, we get J = [4600N/s*t^2 - 3833N/s^2 * t^3] on boundaries 0 to 0.8s, so the impulse is (in magnitude), by evaluating the function at tf= 0.8s and ti = 0 we get the answer to (a) (a) J = 981 Ns

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