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 56.0-kg athlete jumps down onto the platform from a height of 0.670 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 up

(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