Question

A block slides down a ramp from rest. The block travels 7.19 m/s at the bottom of the ramp and has a mass of 2.98 kg. Assuming no friction, what is the height of the block off the ground at the top of the ramp?

Answer 1

As we assume that there is no friction, we can apply the law of conservation of energy to two different moments of the block's movement:

The energy at the top is $E_{kinetic}+E_{potential}=mgH$, as the velocity at the top is zero (block is initially at rest)

The energy at the bottom is $E_{kinetic}+E_{potential}=\frac{mv^2}{2}$, the block has descended, but gained a velocity.

Thus, by the energy conservation, $\frac{mv^2}{2}=mgH; H=\frac{v^2}{2g}; H\approx 2.63m$ (where i took $g=9.8 m/s^2$).