Hi. So here is a problem that is a law of conservation of momentum type of problem. And so in this case we have two footballers that are running towards each other at different velocities and they have different masses, and when they collide they hold onto each other and you're asked, assuming that we're ignoring the friction and so forth, what is their combined velocity after they collide?
So let's quickly draw... as the situation. So here is my first footballer, here is my second footballer.
We know this footballer here was 100 kilograms and they're moving at 5 meters per second in that direction. The other footballer is 70 kilograms and they're moving in that direction at 4 meters per second. So what do we do now?
Well we basically write down the formula for the conservation of momentum and that says that m1 u1 plus m2u2 is equal to m1v1 plus m2v2. That is the total momentum before the collision in a closed system is equal to the total momentum after the collision. So now what we do is we sub things in and so our mass one here is 100 and we multiply by their velocity which is going to be 5. The other footballer has a mass of 70 kilograms. But their velocity is 4 meters per second, but it's going in the opposite direction, so we have to multiply this by negative 4. Now, they hold together, so what we can do is we can combine their masses and treat it as one single mass. So what we have here, the combined mass is 170, and of course they're going to have a common velocity, which is going to be v. Now, when you calculate that out, you're going to get 500 minus 280 is equal to 170 v. You can see v is now going to be equal to 220 over 170, and when you calculate that out, you're going to get 1.3 meters per second.
Notice here this is positive, so that means they're moving in that direction like so. Now if you put on your conceptual, your common sense type of hat, you'll know that because this person is heavier and moving at a higher velocity than this person over here, that they're going to stick together and they're going to move continually in that direction. That makes sense. And so therefore, a positive 1.3 meters per second makes sense. Don't forget to draw the arrow to show you the direction, because momentum and velocity are vectors, which means that you need to both mention the size and direction of the thing you determined.
My name is Paul from Physics High. Take care. Bye for now.