Explanation:
You can solve this with kinematics or with energy. It looks like you want to use energy.
Energy is conserved, so:
initial energy = final energy
Kinetic energy = potential energy
1/2 m v² = m g h
1/2 v² = g h
h = v² / (2g)
If we double the velocity:
H = (2v)² / (2g)
H = 4v² / (2g)
H = 4h
So the new height is 4h.
