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Well, let's see how do we solve this, first I want to identify
where is that roller coaster will be going the fastest and the answer is when it's down here.
This is the lowest point in the roller coaster and therefore the point with the lowest potential energy,
which means the high is kinetic energy and let's see, down here, what kind of energy it does have.
It has kinetic energy. I know it's going to be moving down here and it didn't have
a little bit of potential energy if I'm using the ground as my reference point for zero, so let's see.
Energy is conserved means energy appear equals energy down here.
Roller coaster starts at rest, which means it starts with only potential energy.
I think we're going to call this h₁ to distinguish it from this h over here.
By the time it gets to the bottom, it still has a little bit of potential energy and it has kinetic.
We know motion doesn't depend on mass and luckily the mass is cancelled out.
I can do a little bit of massaging of this equation to get into this form for v²
and to solve for velocity, I just take the square root and look at that.
All that matters, the only way that height comes into this equation is through the change in height, h₁-h₂,.
This is really pointing out the fact that we can choose our zero point anywhere
and all that matters is the change in height.
Well let's plug in our numbers, when I do this I get a very nice number, I get the √900
which is exactly 30 m/s.