A small block of mass m slides to the left on a frictionless, horizontal surface with speed v. Then, the block slides up a rough ramp that has an incline angle of ̑. The coefficient of kinetic friction between the ramp and box is ̑. The acceleration due to gravity is g.
What is the height h of the block when its speed up the ramp equals cv, where 0 < c < 1?
h = (1 - c^2)v^2 / (2g(1 + ̑ cot(̑)))