A 55kg person pushes on the floor with 800 N of force for 0.25 seconds. How high do they jump off the ground?

Question

I know how to find acceleration but I can't find distance.

Answer 1

change in momentum = force * time

force up = 800 -55(9.81)
= 260 N net up force

so
momentum = m Vi = 260*.25 = 65
so
Vi = 65/55 = 1.18 m/s up

(1/2)mVi^2 = m g h
h = Vi^2/[2(9.81)] = .071 meters
= 7.1 cm

Answer 2

I haven't learned momentum yet, is there any way to do it with only Forces and F=ma as well as kinematics?
Thanks

Answer 3

Not really.
I bet you have heard the word "Impulse"
that is force * time
which is change of momentum

F = m a = m dv/dt
so
F dt = m dv = "impulse"

but m dv is change in m v
and m v is "momentum
therefore
F * time = change in momentum = impulse