Solve the equations

Question

1/2mv2 + 1/2Iω2 = mgh and v = rω
for the speed v using substitution, given that
I = mr2
and
h = 4.20 m.
(Note that mass m and radius r will both cancel, so their numerical values aren't required.)
m/s

Answer 1

This is Algebra. Surely you are not having difficulty with this in AP Physics.

1/2 mv^2+1/2 mr^2*V^2/r^2
1/2 m(v^2+v^2)=mv^2

v= sqrt(gh)

Now note something about this. If the object had just fell(no rolling)
v would have been sqrt(2gh)

What heppened, is that energy split equally into rolling, and translational motion.