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 half double triple quadruple its kinetic energy at the top. The car has 450 900 1,800 3,600 joules of kinetic energy at the bottom of the hill.

Answer 1

The answers are quadruple and 1,800 joules, respectively. 

The formula of Kinetic Energy is:
$KE= \frac{1}{2}mv^{2}$

Where:
KE=Kinetic Energy
m = mass
v = velocity

The given are as follows:
m =100Kg
v at the top to the bottom of the hill = 3m/s
v the bottom of the hill= 3 m/s x 2 = 6m/s

So it goes from the top to the bottom so let's calculate the top first before we do the bottom. 

Plug in the values for the kinetic energy from the top to the bottom of the hill:
$KE= \frac{1}{2}mv^{2}$
     $= \frac{1}{2}(100Kg)(3m/s)^{2}$
     $= \frac{1}{2}(100Kg)(9m^{2}/s^{2})$
     $= \frac{1}{2}(900kg.m^{2}/s^{2})$
     $= 450 kg.m^{2}/s^{2}or 450Joules$

So from the top to the bottom of the hill, the kinetic energy is 450 Joules. 

Next we do the kinetic energy from the bottom of the hill, so we do the same and use the velocity that corresponds to it:

$KE= \frac{1}{2}mv^{2}$
     $= \frac{1}{2}(100Kg)(6m/s)^{2}$
     $= \frac{1}{2}(100Kg)(36m^{2}/s^{2})$
     $= \frac{1}{2}(3,600kg.m^{2}/s^{2})$
     $= 1,800 kg.m^{2}/s^{2}or 1,800Joules$

From the bottom of the hill, the kinetic energy of the roller coaster is 1,800Joules. This is 4 times the amount of energy than the previous. If you want to check, you can do this by dividing the KE from the bottom by the initial KE. 

$\frac{1,800Joules }{450Joules} =4$

Answer 2

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