Work And Energy 3

Question

A child and sled with a combined mass of 43.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 4.00 m/s at the bottom, what is the height of the hill?

Answer 1

Since there is no friction, the total mechanical energy is conserved.   At rest, the energy is PE, and at the bottom of the hill, which is the reference height, PE - 0;

 

Accordingly PE initial = KE final =  1/2 (43kg) * (4m/s)² =  344 Joules.    344 J =43 * 9.8 *h   This is easily solved to yield the height of the hill.   About 0.8 meters.