Question

A roller coaster starts at ground level and rises up 139 m above the ground on the first hill. What is the maximum speed it can have when it rolls down to the ground level?

Answer 1

Height of the roller coaster as it rolls down to the ground level = 139 m

We need to find what could be the maximum velocity as it rolls down to the ground level.

For that we will use, law of conservation of energy.

Now at the top of the hill, the velocity will be zero, so no kinetic energy. Hence, net energy will be present only in the form of potential energy

At the bottom of the hill i.e. the ground level, all potential energy is converted into kinetic energy. Hence net energy present only as kinetic energy.

So, we will equate them both.

Potential Energy at top of hill = Kinetic Energy at bottom of hill

So,

mgh = 1/2 mv2

Where,

m = mass of roller coaster

g = acceleration due to gravity = 9.8 m/s2

h = height = 139 m

v = velocity at the ground level

So, =

v = 52.196 m/s

Hence the maximum velocity the roller coaster can have as it rolls down to ground level is 52.196 m/s