Arock is dropped from rest from a height h above the ground. it falls and hits the ground with a
speed of 11 m/s. from what height should the rock be dropped so that its speed on hitting the ground
is 22 m/s? neglect air resistance

Use energy conservation, since no energy is lost it must be constant.

E = 0.5mv² + mgh

At release the velocity v = 0 and the height is h.

E = 0 + mgh

At impact the height h = 0 and the velocity is v.

E = 0.5mv² + 0

Since the energy E is conserved:

0.5mv² = mgh

the mass m cancels and the equation becomes:

0.5v² = gh

h = 0.5v²/g

when g = 9.81 and v = 22:

h = 24,66