You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. (a) If you catch the ball, with what speed do you and the ball move afterward?

Video transcript

everyone. Welcome back in this video. We have a problem where we have a player on roller skates and there's gonna be a ball coming towards them horizontally. We're gonna catch that ball. And we want to figure out what the speed of the ball and the player is after the catch. Now, we're told that the roller skates are on our frictionless. We don't have to worry about friction. Let's go ahead and draw our system and fill in the information we know. So before the catch, we know we have a ball traveling horizontally, we're gonna take right to be the positive. X direction and it's traveling towards the player. Okay? We're told that the player weighs 68 kg and that they're standing. So standing means not moving. So the velocity of the player initially is going to be zero. We're also told that the ball has a mass of 450 g. And we want to be careful here, the mass of the player is given in kilograms. The mass of the ball is given in grams. So, we're gonna go ahead and convert the 450 g to 0.45 kg. So that we have consistent units. Okay, We're also told the speed of the ball. So we're gonna say the velocity of the ball initially is 12.5 m per second. Let me just Alright now, after the catch the players gonna hold onto the ball. Okay, So we have the player and they're holding onto the ball. So, instead of having two separate masses, we're just gonna have one final mass and that's gonna be the mass of the player plus the mass of the ball. So that's going to be 68.45 kg. Now we don't know what the speed is here, that's what we're trying to figure out. What is that final speed. And that's the question here. The speed of the ball and the player after the catch. Okay. What we want to recognize is that's just one value. Okay the ball, the player is holding the ball so they're gonna be moving with the same speeds. We don't need to find two different speeds for them. It's one value that we're looking for. So let's go ahead with our conservation of momentum. The momentum in the system initially is going to be equal to the momentum in the system. At the end, the momentum in the system initially consists of two parts. We have the momentum of the ball, We have the momentum of the player. That's the momentum of the player plus the momentum of the ball initially is going to be equal to this momentum of the system. Finally we're just gonna call that P. F. Okay so the final momentum, it's just gonna be the momentum of the player and the ball together. Alright now let's recall what is momentum while we know momentum is the mass times the velocity. Okay so for each of these components we have mass times corresponding velocity and on the right hand side, That final momentum, we have the final mass, which is the total mass of the ball and the player together, and the final velocity, which is what we're looking for. We're looking for the speed of the player and the ball after the catch. All right, let's fill in the values we know. So we know the mass, 68 kg of a player. We know their initial velocity is zero, so that term is just going to go to zero. We know the mass of the ball is 0.5 kg and its velocity is 12.5 m/s initially. And on the right hand side, the final mass, the mass of the ball player together 68.45 kg. And this value VF which we're looking for. Alright, simplifying on the left hand side, 5.625 kilogram meters per second. Okay, and on the right hand side we still have 68.45 kg, times that value b. f. Alright, so dividing in order to isolate VF the units of kilograms will cancel. We'll be left with V. F is equal to 0. m per second. And that's great. That's the units for velocity that we would want. All right, and we notice that this is positive, the velocities positive. We've chosen right to be the positive X. Direction. And so, what that means is after the catch the player and the ball are going to be moving to the right and that makes sense. The players on roller skates when they catch the ball, it's gonna push them backwards a little bit. Alright, so to wrap this question up, we have to realize that they're asking for speed, not velocity, and let's remember speed is that value VF, And it's going to be the absolute value of the velocity, and in this case it's just going to be the same 0.082, m/s. Okay, So this is our speed at the end that we were looking for and that's gonna be answer. C Alright, thanks for watching. See you in the next video.