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: _________ m (round to the nearest hundredth)

Answer 1

Given:

The mass of the child and the sled is,

`m=25.2\text{ kg}`

The child acquires a speed at the bottom of the hill is,

`v=6\text{ m/s}`

To find:

The height of the hill

Step-by-step explanation:

The potential energy at the top of the hill will be converted to the potential energy at the bottom of the hill. So for the hill of height 'h', we can write, the potential energy as

`PE=mgh`

The kinetic energy is

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

So,

`\begin{gathered} mgh=(1)/(2)mv^2 \\ h=(v^2)/(2g) \\ h=(6^2)/(2*9.8) \\ h=1.84\text{ m} \end{gathered}`

Hence, the height of the hill is 1.84 m.