Question

A kiddie roller coaster car has a mass 100 kilograms. At the top of a hill, it’s moving at a speed of 3 meters/second. After reaching the bottom of the hill, its speed doubles. The car’s kinetic energy at the bottom is its kinetic energy at the top. The car has joules of kinetic energy at the bottom of the hill.

Answer 1

The car’s kinetic energy at the bottom is 4 times its kinetic energy at the top. The car has 1800 joules of kinetic energy at the bottom of the hill.

Step-by-step explanation:

The kinetic energy of the car is given by:

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

where m is the mass of the car and v its speed.

First of all, we see that the kinetic energy is proportional to the square of the speed: since the speed of the car at the bottom of the hill is twice the speed at the top of the hill, then the new kinetic energy must be
`2^2=4` times the kinetic energy at the top.

We can explicitely calculate it by using the formula.

At the top of the hill:

`K=(1)/(2)(100 kg)(3 m/s)^2=450 J`

At the bottom of the hill, the speed has doubled, so it is 6 m/s; therefore, the kinetic energy is

`K=(1)/(2)(100 kg)(6 m/s)^2=1800 J`

Answer 2

A kiddie roller coaster car has a mass 100 kilograms. At the top of a hill, it’s moving at a speed of 3 meters/second. After reaching the bottom of the hill, its speed doubles. The car’s kinetic energy at the bottom is quadruple its kinetic energy at the top. The car has 1,800 joules of kinetic energy at the bottom of the hill.