Deriving Roller Coaster Speed Equations at Bottom of Slope

[kraigandrews]

Homework Statement

A roller coaster is at the top of a slope moving very slowly. There are three lengths in this problem: h = 53 m is the height of the hill; D = 65 m is the length of the hill; L = 43 m is the length of the coaster. Derive an equation for the speed v1 when the first car reaches the bottom of the slope. (The hill has constant slope.) Derive an equation for the speed v2 when the last car reaches the bottom. What is the ratio v1/v2?

Homework Equations

all energy equations

The Attempt at a Solution

To be honest I don't really know where to start. I know how to solve this to find the velocity at the bottom of the hill if it were considered a point particle, but not for the things that the question is asking. So any advice or help would be greatly appreciated.

 

[kuruman]

Treat the roller coaster as a point particle situated at the center of mass.

 

[BruceW]

To be honest I don't really know where to start. I know how to solve this to find the velocity at the bottom of the hill if it were considered a point particle, but not for the things that the question is asking. So any advice or help would be greatly appreciated.

You should really give some kind of attempt before asking for help. They are quite strict about that here.

 

[kraigandrews]

sorry, here is what i have so far:
if we are to treat it as a point particle moving down the hill at the bottom it will have v=(2gh)^1/2, now from there my next idea was to find how far the front would travel in relation to back then find the ratio.

 

[kuruman]

Where is the point mass when the front of the roller coaster reaches bottom?