A 28 kg boy sitting on a 12 kg go-kart starts from rest down a hill of height 9 m. What is the combined speed of the boy and go-kart when they reach the bottom of the hill?

Question

A 28 kg boy sitting on a 12 kg go-kart starts from rest down a hill of height 9 m.

What is the combined speed of the boy and go-kart when they reach the bottom of the hill?

Answer 1

Let

m = 40 kg be the combined mass of the boy and the go-kart,

h = 9 m be the height of the hill,

g = 9.8 m/s² be gravitational acceleration,

v (to be calculated) be the speed at the bottom of the hill.

The initial potential energy, mgh, gets converted into the final kinetic energy, mv²/2.

mv²/2 = mgh

v = √(2gh)

Substituting actual numbers,

v = √(2 x 9.8 m/s² x 9 m) = 13.3 m/s

Note than the speed does not depend on the mass m.

That would play a role only if friction were taken into account.