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## Homework Statement

A roller coaster starts at the top of hill that is 10 m high. If it is to barely make it to the top of a second hill that is 20 m high, how fast must the initial speed of the roller coaster be? Assume that the roller coaster is frictionless.

## Homework Equations

KE = 0.5mv^2

PE = mgh

## The Attempt at a Solution

mgh=0.5mv^2

gh = 0.5v^2

v = sqrt(2gh)

v = sqrt(2*9.81*20)

v = 20 m/s needed at bottom of second hill.

mgh=0.5mv^2

gh = 0.5v^2

v = sqrt(2gh)

v = sqrt(2*9.81*10)

v = 14 m/s at bottom of hill if initial velocity at top of first hill is 0m/s.

20 m/s - 14 m/s = 6 m/s

6 m/s is the velocity of the roller coaster at the top of the first hill.

Does that look right?