Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 7.50 kg, is sliding to the left at 5.00 m/s, while the other, of mass 5.75 kg, is slipping to the right at 6.00 m/s. They hold fast to each other after they collide. (a) Find the magnitude and direction of the velocity of these free-spirited otters right after they collide.

Video transcript

Hey everyone, welcome back. So today we have this problem, we have two kids, they're on a slippery surface and we're told the surface is frictionless, so that's going to be important. We don't need to deal with friction. And the kids are jogging and sliding towards each other and they're gonna collide. We're told that after the collision the kids are gonna hold on to each other. Okay, So this is a little bit different than some of the other collision problems. Instead of colliding and then continuing separately, they're going to collide and continue together. Okay, So with collision problems like this, what we want to do is we want to draw a diagram of what's going on before and after the collision and fill in any of the details that were told. So before the collision, we have the first child here. Okay. And we're told that the child is 18.2 kg. So they have a mass 18.2 kg. Alright. And we're told that they're sliding east 4.3 m per second. Okay? So we're going to say they're going to the right with a speed or velocity, We're gonna call the velocity of the first child initially to be 4.3 m/s. Okay, So what we're gonna do is we're gonna call to the right the positive direction, positive X direction, and that's gonna be the direction of east. So we're gonna keep that for a problem. And now, before the collision, we also have the second child. So our system contains both Children. The second child has a mass of 16.3 kg. And we're told that they're traveling west 3.8 m per second. Okay, so they're actually gonna be going to the left 3.8 m/s. And now this is a velocity we're talking about. So they're going in the opposite direction, they're traveling west. So that's actually going to be a negative velocity. Ok? After the collision, we're told that the kids stick to kind of hold onto each other, stick together. So we will have something like this where we have a child one And child two stuck together. So what that means is that the mass after the collision? So the final mass is actually going to be the mass of the first kid plus the mass of the second kid, it's gonna be 18.2 plus 16.3 is going to be 34.5 kg. Okay. And we don't know what their final speed will be and that's what we want to find out. We want to determine the velocity magnitude and direction after they have collided. And it's important to note that the velocity in direction of the sorry, the magnitude and direction of the velocity of the kids, it's going to be the same for both kids because the kids are holding onto each other. So we're just one value that we need to find. Okay, so let's start. We know we have conservation of moment. So we know that the initial momentum in our system is going to be equal to the final momentum in our system. Well, what does our system consist of before the collision? Our system has two Children. So the momentum is going to be the The momentum of child one plus the momentum of child to initially and after the collision we just have one final momentum. Okay, because we have one, the kids kind of become one object moving together. Alright, now, let's recall what momentum is, momentum is going to be mass times velocity. So for each of these momentum's we have mass and the corresponding velocity mass and the corresponding velocity. And again in the case of the final momentum we have the final mass which is the total mass of the two Children and that final velocity the velocity that the kids will be moving together at the end. Alright, so let's fill in the details of what we know, We know that the massive child one is 18.2 kg and their velocity is 4.3 m/s For child to we have 16.3 kg. Now, momentum is a vector just like velocities who are putting our velocity in here. It's important to include the sign to indicate the direction. So -3.8 m/s. Okay, and then our final mass 34.5 kg and v. f. again the velocity that we're looking for. Alright, so let's go ahead and simplify and see what we get here. So on the left hand side we're going to get 78. minus 61.94. Okay. And the units here are gonna be kilogram meter per second. And on the right hand side we're still gonna have 34. kg times v. Alright, so on the left 16.32 kg meters per second. And on the right, 34.5 kg. Now, in order to sulfur VF, we need to divide by 34.5. Um And here we have kilograms. So the kilogram unit on each side is going to cancel, and we're just gonna be left with the unit of meters per square meters per second. Sorry. So the final velocity, the f is going to be 0.473 m/s. Okay, so that is the answer we're looking for now. We just need to go and interpret it. So we know that the magnitude of the velocity is gonna be 0.473 m per second. So, when we're looking at our answers, we know we've narrowed it down to either E or F. Now the velocity is positive. We know that we've chosen the positive direction to be east. So we know that we're going east. So the solution is in fact f where we have a magnitude of 0.473 m per second. We're traveling east. Alright. Thanks for watching. I hope this helps see you next time.