Answer: in the explanations.
Explanation:
Assuming no friction losses, when the center of mass of the roller coaster falls a vertical height h from the initial hill it will have a kinetic energy equal to the gravitational potential energy stored in the height (h).
It can be expressed as
W= mgh
Where
W= is the gravitational potential energy at the top of the hill.
m= mass of the roller coaster
g= acceleration due to gravity (9.8m/s² )
h= vertical height from the hill.
Kinetic energy of the roller coaster is ;
KE = ½ mv²
Where
v= speed of the roller coaster.
Since we assumed that there was no friction losses, energy is conserved. It's therefore expressed as;
W= KE
Thus,
mvh = ½ mv²
Mass will cancel out each other, leaving.
v = √2gh
