00:01
Okay, in this problem we have a person swinging down to rescue another person and then swinging up to safety.
00:09
So we have our rope here and we have barbara over here and james down here.
00:25
So she's going to swing down, grab him, and then they're both going to swing up.
00:30
And we want to know how high up are they going to be able to make it.
00:38
Off the ground, so some value h.
00:42
Right, and initially she's this distance r off the ground, where r is the length of the rope, because we're told that the rope starts horizontal.
00:59
Okay, and let's draw the ground here.
01:07
And we'll just measure these distances relative to the ground instead of like relative to the center of mass or anything.
01:19
Okay.
01:22
So what kind of principles do we have going on? oh, let's label their masses.
01:26
Let's do m1 for barbara and m2 for james.
01:32
So we have some energy being conserved, right? we have a collision as well because she swings down, grabs him, and then they swing away.
01:45
So we can't ignore the collision.
01:49
So we're going to have to do a good thing.
01:50
Combination of energy and momentum.
01:55
So energy and momentum.
01:58
And what we can do here is think about some different speeds.
02:09
So let's call the speed that she's moving at when she gets to the, when she is about to hit james, let's call that v1.
02:21
And after she hits him, they move together.
02:26
At a speed of v2.
02:28
So v1 is right before she hits him, v2 is right after she hits it.
02:32
Okay.
02:33
So given a speed of v2, we can now solve for the height that they'll go, right? if we do conservation of energy, so the initial, i'll just do i for initial energy will be when they're down here right after the collision, and the final energy will be when they're up at that final height.
02:57
So initially, what energy do they have? one half, m1 plus m2 times their speed squared.
03:12
And what energy do they have at the top? m1 plus m2, gh, right? so their kinetic energy is turned into potential energy.
03:23
Again, v2 is the speed right after their collision.
03:31
Okay...