00:02
Okay, here is someone standing on a bank holding onto a rope that is 20 meters long and 35 degrees from the vertical.
00:10
In this case, the vertical is a tree, and they're about to jump into a pond.
00:15
And we need to find the energy of the person holding onto the rope in order to solve for their speed at the bottom of the swing.
00:25
So let's solve for our initial energy, which is going to be equal to our kinetic energy and our gravitational potential energy.
00:39
In this case, the person is at rest standing on the bank, so they have no kinetic energy, just gravitational potential energy, which we know is equal to mass times gravity times height.
00:56
And in order to find our height, we have to do a little bit of trigonometry.
01:03
So we have, this is the rope, 20 meters long, and this angle is 35 degrees.
01:19
In order to find the height of the person standing there, we are going to solve for this side.
01:27
So to do that, we set this up as cosine of 35 degrees.
01:34
Equals x our initial height over 20 meters and that gives us a value of 16 .38 meters.
01:57
So we have an initial gravitational potential energy of mass times 9 .8 times 16 .38.
02:11
And now we are going to find the final energy of the person at the bottom of the swing...