Question

A sled is initially at rest at the top of a hill at an elevation 55.0 m higher than the elevation at the bottom. Find the speed of the sled after it slides without friction down the slope to the bottom.

Answer 1

32.8 m/s

Step-by-step explanation

Given:

• The initial elevation of the sled, h = 55.0 m

,

• There is no friction

Find:

• The speed of the sled at the bottom of the hill, v

By the Law of Conservation of Energy, since there is no friction,

`PE-KE=0`

Therefore,

`PE=KE`

The expressions for the gravitational potential energy, PE, and the kinetic energy, KE, are,

`mgh=(1)/(2)mv^2`

We have to find v, so solving the equation above for v,

`v=\sqrt{(2mgh)/(m)}=√(2gh)`

As we can see, it does not depend on the mass of the sliding object. Replace the known values and solve,

`v=√(2\cdot9.8m/s^2\cdot55.0m)\approx32.8m/s`

Hence, the speed of the sled at the bottom of the hill is 32.8 m/s, rounded to the nearest tenth.