Question

A child and sled with a combined mass of 57.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 2.40 m/s at the bottom, what is the height of the hill?

Answer 1

The height of the hill is 29.3 cm.

Step-by-step explanation:

Given that,

The combined mass of a child and sled, m = 57 kg

Initial speed of the sled, u = 0

Speed at the bottom of the sled, v = 2.4 m/s

We need to find the height of the hill. The energy at the bottom and the top will remains the same due to the law of conservation of energy. So,

`mgh=(1)/(2)mv^2\\\\gh=(1)/(2)v^2\\\\h=(v^2)/(2g)\\\\h=((2.4)^2)/(2* 9.8)\\\\h=0.293\ m\\\\h=29.3\ cm`

So, the height of the hill is 29.3 cm. Hence, this is the required solution.

Answer 2

Step-by-step explanation:

mass of sled, m = 57 kg

initial velocity, u = 0 m/s

final velocity, v = 2.4 m/s

Let h be the height of the hill.

Change in potential energy = change in kinetic energy

m x g x h = 0.5 x m x (v² - u²)

9.8 x h = 0.5 x 2.4 x 2.4

h = 0.3 m