Using the conservation of energy, find the velocity vB of the block at the bottom of the ramp.
Express your answer in terms of some or all of the variables m, vand H and any appropriate constant.
Answer
at the top the energy is
1/2mv^2 + mg/h
down before the block hits the ground
1/2mvb^2 = 1/2mv^2 + mg/h
1/2vb^2 = 1/2v^2 + g
vb^2 = v^2+2gh
vb = sqrt(v^2+2gh)
mgh + 1/2 mv^2 = 1/2 mvf^2
vf^2 = 2gh + v^2
vf = sqrt(2gh + v^2)