Answer:
19.8 m/s
Explanation:
Assuming the car starts from rest, initially when it is at the top of the hill all the mechanical energy of the car is just potential energy, given by:
[tex]U=mgh[/tex]
where
m = 100 kg is the mass
g = 9.8 m/s^2 is the gravitational acceleration
h = 20 m is the height
Substituting,
[tex]U=(100 kg)(9.8 m/s^2)(20 m)=19,600 J[/tex]
At the bottom of the hill, all this energy has been converted into kinetic energy (because energy cannot be created or destroyed, but only transformed). Therefore, the kinetic energy of the car is:
[tex]K=\frac{1}{2}mv^2=19,600 J[/tex]
where
m = 100 kg is the mass of the car
v is the speed of the car at the bottom of the hill
Re-arranging this equation, we can find the value of v:
[tex]v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(19,600 J)}{100 kg}}=19.8 m/s[/tex]
