00:01
So here we're dealing with a roller coaster.
00:02
And we want to find two things.
00:05
We want to find the height of the first hill at point a so that the cart on the roller coaster can go through the loop at point b.
00:15
And we also want to find the velocity of the cart at point c after the loop.
00:21
So we can first break this down just by looking at points a to b.
00:28
So from point a to point b, we have a height, which is what we're looking for.
00:34
So there's a potential energy.
00:35
And the cart, once it goes down the hill, it begins to move.
00:39
So there's a kinetic energy.
00:41
So that means we can use the conservation of energy equation.
00:47
And again, we're looking at from point a, the top of the hill, which we're looking for, to be inside the loop.
00:56
So then we have.
00:59
So the initial kinetic energy is zero, because there.
01:02
The cart starts at rest.
01:04
So we just have the initial potential energy, which is mass times gravity times h .a equals the kinetic energy of point b, one half mvb squared, plus the potential energy at b, which is m, g, hb...