Question

A 64-kg person riding on a roller coaster starts at rest and reaches a final speed of 26 m/s at the bottom of its first hill. What is the roller coasters height?

Answer 1

34.5 m

Step-by-step explanation:

According to the law of conservation of energy, the mechanical energy of the person at the top of the hill must be equal to the mechanical energy at the bottom. However:

- the mechanical energy at the top is just gravitational potential energy, since the person is at rest, so the kinetic energy is zero

- the mechanical energy at the bottom is just kinetic energy, since the height of the person has becomes zero

So, the initial gravitational potential energy of the person must be equal to the final kinetic energy of the person:

`U=K`

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

where

m = 64 kg is the mass of the person

g = 9.8 m/s^2 is the acceleration due to gravity

h is the initial height of the roller coaster

v = 26 m/s is the final speed

Solving for h,

`h=(v^2)/(2g)=((26 m/s)^2)/(2(9.8 m/s^2))=34.5 m`