Question

A child and sled with a combined mass of 50.2 kg slide down a frictionless hill that is 8.38 m high. If the sled starts from rest, what is its speed at the bottom of the hill?

Answer 1

here we can say that since the hill is friction less So total energy is now conserved

we can use the energy conservation principle now

$U_i + KE_i = U_f + KE_f$

here we can say that initial KE is zero as the child and sled is at rest

and the final potential energy will also be zero as the child will reach the bottom

So here we can say

$mgh + 0 = 0 + \frac{1}{2}mv^2$

$v = \sqrt{2gh}$

$v = \sqrt{2*9.8*8.38}$

$v = 12.8 m/s$

so final speed will be 12.8 m/s