Question

a 60.00-kg athlete leaps straight up into the air from a trampoline with an intial speed of 9.0 m/s. The goal of this problem is to find the maxiumum height she attains and her speed at half maximum height. what are the interacting objects and how do they interact?

Answer 1

I do not see any interacting objects except the earth (providing gravitational force) and the body. The mass is also irrelevant since it will cancel.

F = m a = - m g
so
a = -g

Vi = +9 m/s
g = -9.81 m/s^2

V at top = 0
V = Vi - 9.81 t
so
t = 9/9.81 = .917 seconds rising

Max h = height when V = 0
= Vi t - (1/2) g t^2
= 9 (.917) - 4.9 (.917)^2
= 8.26-4.13 = 4.13 meters

speed at 2.06 meters?
2.06 = 9 t - 4.9 t^2

4.9 t^2 - 9 t + 2.06 = 0

t = [ 9 +/- sqrt (81-40.4) ] /9.81
= [9 +/- 6.37 }/9.81
use either time, one is on the way up, the other on the way down, same speed, opposite directions. for example use - sign
t = .268 seconds
V = 9 - 9.81 (.268) = 6.37 m/s