Question

A roller coaster car starts at Point A at a height of 100 m. When it reaches Point C on a lter hill, it is moving 15 m/s. What is its height at Point C assuming no friction? (88.5 m)

Answer 1

the answer is in the parenthesis i just need to know how figure it how. and here is the picture that goes with the question

Answer 2

This is all energy. When you have a height (h) then you have a potential energy of mass times gravitational acceleration times height (mgh). This is the only energy you have on A since it starts from rest. On B you have a new height (h2) which means you have a potencial enery (mgh2) but thats smaller than the one you had on A and energy has to be conserved, therefore you need an energy of the velocity (v) it has at B which is one half of mass times velocity squared (1/2mvpower2) so if you massage that you get:\[mgh=mgh _{2} + \frac{ 1 }{ 2 }mv ^{2} \rightarrow h _{2}=h-\frac{ v ^{2} }{ 2g }\]You get that answer by replacing with this values:\[h _{2}=100m-\frac{ (15\frac{ m }{ s })^{2} }{ 9.8\frac{ m }{ s ^{2} }2 }=88.5m\]