A block of mass m slides across a frictionless floor and then up a frictionless ramp. The angle of the ramp is θ and the speed of the block before it starts up the ramp is v0. The block will slide up to some maximum height h above the floor before stopping. Show that h is independent of m and θ by deriving an expression for h in terms of v0 and g.
Use energy conservation to solve this.
Moving block's Kinetic Energy: KE = 1/2*m*Vo^2
Stationary block's Potential Energy: PE = m*g*h
Energy conserved means: KE = PE (remember - the floor and ramp are frictionless)
1/2*m*Vo^2 = m*g*h
Isolate h and you have it.