A 90kg stuntman falls from a

Question

building that is 80 meters tall. (Vo = 0)Fortunately, the stuntman is attached
to a cable that is wrapped around a flywheel (massive spool), with a radius of 0.5m. If the man takes 8 seconds to reach the ground:
(a) what is the moment of inertia of the flywheel?
(b) What is the moment inertia if the radius of the wheel was 1m?
(c) What is the mass of the flywheel in each case?

Answer 1

Ke of man = (1/2) m v^2
Ke of flywheel = (1/2) I w^2 = (1/2)I (v/r)^2
Total Ke = (1/2) m v^2 + (1/2) (I/r^2)v^2

potential energy decrease = m g h = 90(9.81)(80) = 70,632 Joules

constant acceleration
average v = 80 meters/8 seconds = 10 m/s
initial v is zero so final v is 20 m/s

so
70,632 = (1/2)(20)^2 [ m + I/r^2 ]

I think you can take it from there.