00:01
So we have two astronauts facing each other in a vacuum.
00:06
We've got m1, m2, and the first one throws a ball, mb, at a speed v.
00:16
Now to conserve momentum, let's say that this guy has a speed u1.
00:22
We have m1u1 equals mbv.
00:27
So u1 is going to be mb over m1 times v.
00:34
So at this first stage, we have mb over m1v, the ball going at speed v, and this astronaut at speed zero.
00:47
This has mass m1, mb, and m2.
00:51
So now let's say that the m2 catches the ball.
00:58
So now this guy is going mb over m1v, m1, and then we've got this guy plus the ball with mass m2, mb.
01:10
Now to conserve momentum they're going in a speed u2 which is such that m2 plus mb u2 is equal to mb v.
01:27
So u2 is equal to mb over m2 plus mb times v.
01:38
So now the guy throws the ball at a speed v relative to the thrower.
01:46
So this guy is still moving mbv over m1.
01:52
The ball is thrown at a speed mb relative to the thrower, a speed v relative to the thrower.
02:00
So its speed is going to be the speed in the positive direction.
02:05
So this is in the negative direction, so it gets a minus sign.
02:09
This is going to be in the positive direction.
02:12
So well, in the negative direction we're going to get minus, so v minus mb over m2 plus mb v which is equal to minus v times m2 minus mb so that m2 plus mb minus mb is m2 over m2 plus mb so that's the speed of the ball now this guy is going to be moving this way with a speed u3 and we're going to have the the momentum of the of the guy ball system.
02:55
So we're going to have minus v m2 mb over m2 plus mb plus mb plus m2 u3 is equal to the momentum that they had before together, which is mbv.
03:21
So now we can solve for u3.
03:23
U3 is bv.
03:29
Plus m2mb over m1 plus m2 v, divided out by m2.
03:42
So this is going to be v times mb times m1 plus 2m2, because we're going to get an m1 plus m2 and an m2 divided by m1 plus m2.
04:03
So now let's write out what this situation looks like once again.
04:07
So you've got this guys with m1.
04:09
Mass m1, going in a speed minus mb over m1v.
04:15
We've got the ball coming towards him at a speed minus v, m2 over m2 plus mb, and it's got a mass m2, no, mb.
04:36
And we've got the other astronaut, mass m2, moving away at a speed vmb, m1 plus 2, m2, divided by m1 plus n2.
04:52
So now we've got one more catch and we're going to have the astronaut 1 moving at a speed of minus u4 and they'll have caught the ball so that mass is going to be m1 plus mb and we'll have astronaut 2 moving this way at the speed that they were moving before vmb m1 plus sorry that should be mb shouldn't it no m1 plus no m1 plus 2m2.
05:30
Yeah, so m1 plus 2m 2 divided by m1 plus m2.
05:42
There should be an m2 in here as well.
05:59
Okay, and now what we're going to have is that u4 will include the momentum of all this stuff.
06:05
So m1 plus mb u4 is going to be equal to mb plus mbv plus mbv plus mb...