Question

A child and sled with a combined mass of 25.2 kg slide down a frictionless hill, starting at the top. The sled starts from rest and acquires a speed of 6 m/s by the time it reaches the bottom of the hill. What is the height (in m) of the hill?

Answer 1

Given there is no friction, the law of conservation of energy can be applied. This is:

$\Delta E=0$

For our case, the energy in the beginning will be simply potential, and by the end will be only kinetic. We can write this as:

$mgh=\frac{mv^2}{2}\Rightarrow h=\frac{v^2}{2g}$

For our case, this will be:

$h=\frac{6^2}{2*10}=1.8m$

Thus, the hill has 1.8m