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## Homework Statement

A roller coaster car starts from rest and rolls down a frictionless track, reaching Vf ( final speed) at the bottom.

if you want the car to go two times as fast at the bottom by what fator must you increase the height of the track

## Homework Equations

KE=1/2mv^2

PE=mgh

## The Attempt at a Solution

So according to the conservation of energy

KEi+PEi = KEf+PEf

in this case the KEi = 0 and PEf = 0

so

PEi = KEf

mgh= 1/2mv^2

mass cancels

gh=1/2v^2

2gh=V^2

so v= square root of 2gh

after this i have though to set the equations like this

vf= sqaure root of 2gh

2vf= square root of 2gh

that what i have so far but i dont know how to continue on