Aforce 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 67.0-kg athlete jumps down onto the platform from a height of 0.720 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?

(d) to what height did she jump upon leaving the platform?