Question

A 6 kg cart starting from rest rolls down a hill and at the bottom has a speed of 10 m/s. What is the height of the hill?

Answer 1

h = 5.09 m

Step-by-step explanation:

Applying the Law of conservation of energy to this situation, we can write:

`Kinetic\ Energy\ Gained\ by\ the\ Cart = Potential\ Energy\ Lost\ by\ the\ Cart\\(1)/(2)mv^2 = mgh\\\\h = (v^2)/(2g)`

where,

h = height of the hill = ?

v = speed of cart at the end = 10 m/s

g = acceleration due to gravity = 9.81 m/s²

Therefore,

`h = ((10\ m/s)^2)/((2)(9.81\ m/s^2))\\\\`

h = 5.09 m