Answer:
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.
Explanation:
The kinetic energy of the car is given by:
[tex]K=\frac{1}{2}mv^2[/tex]
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 [tex]2^2=4[/tex] times the kinetic energy at the top.
We can explicitely calculate it by using the formula.
At the top of the hill:
[tex]K=\frac{1}{2}(100 kg)(3 m/s)^2=450 J[/tex]
At the bottom of the hill, the speed has doubled, so it is 6 m/s; therefore, the kinetic energy is
[tex]K=\frac{1}{2}(100 kg)(6 m/s)^2=1800 J[/tex]
