The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track.

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

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