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 62.4-kg athlete jumps down onto the platform from a height of 0.636 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?
b) With what speed did she reach the platform?
c) With what speed did she leave it?
d) To what height did she jump upon leaving the platform?