You are standing on a sheet of ice that covers the football stadi...

Question

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. (b) If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 m/s in the opposite direction, what is your speed after the collision?

Accepted Answer

Hey everyone, welcome back in this video. We're gonna be standing on a slippery surface, it's going to be frictionless. Okay, our colleagues going to throw a ball at us, we're gonna deflect it back towards them. What we want to find out is what is our speed after the collision. Alright, so the first thing we want to do with collision problems like this is go ahead and draw out a diagram of the system both before and after the collision and fill in any of the details that we know. Alright, so we know that we have our colleague here. Okay. And they're going to throw a ball. The ball will be red towards us. Okay? And we're going to be in blue here. Now we know that we are standing. Okay, so stationary, that means our speed or velocity initially is just going to be zero. Hey, standing and our masses 68.5 or sorry, 65.8 kg. All right now, what about the ball? Alright, well, the ball is going to be 550 g. We want to be careful here because the mass of the person is given in kilograms. The mass of the ball is given in grams. We just want to convert this into kilograms so that we have consistent units. So that's gonna be 5500.55 kg. Were told that the ball is going to be going towards us At 7.6 m/s. So it's gonna be going to the right towards us, which is the blue person um with a speed Or a velocity of 7.6 m/s and we're gonna take the right to be the positive X direction. Okay, so that initial velocity is going to the right, so it's going to be positive. Alright, now, after the collision, our colleagues still standing here, we're not giving any information about our colleague. We've deflected the ball back towards our colleague. Okay, So it's gonna go towards the colleague at 11.3 m/s. So now it's going to be going to the left towards our colleague. Okay. And what does that mean about the velocity while we're going to the left, we're going in the opposite direction of our positive X direction. So the velocity is going to be negative. So we have a negative 11.3 m per second. Okay. And the ball is still going to have the same mass of 0.55 kg. And then in terms of us, well, we're gonna have the same mass. Let me just write it up here. We're gonna have the same mass as before. Okay. And we don't know anything about our speed. So, the speed of us at the end, we don't know and that's what we're trying to find. All right? So, let's start when we have a collision problem like this, we know that momentum is conserved. So let's start with our conservation of momentum equation. So we know that the momentum in the system initially is going to be equal to the momentum in the system at the end. Okay. What does our system consist of? Well, in our drawing we have three things in our system. Okay, so we have the momentum of our colleague initially we have the momentum of the ball which we've called one and we have the momentum of us which we've called to. Okay. And after same thing, momentum of the colleague at the end plus momentum of the ball. The end plus the momentum of us at the end. Alright, now let's recall, momentum is going to be mass times velocity. So for each of these terms we're going to have the corresponding mass times the velocity mass times velocity mass times velocity and same thing on the right side, the mass of the colleague, the velocity of the colleague, the mass of the ball. The velocity of the ball at the end and the mass of us, the velocity of a city. Okay, now to notice right off the bat, the information we're given about our colleague is that they're standing there, they're standing there at the beginning, they're standing there at the end. So their velocity or their speed is going to be zero, both before and after. So the terms that talk about the colleague here are just going to be going to zero because the speed and velocity is going to be zero. Okay, so the only two things now we have to worry about in our system are the ball and us. Alright, so let's fill in the values we know. Okay. And we can see here too, this V two F at the end. That's that value we're looking for. Okay, so let's fill in what we know the mass of the ball. 0.55 kg. Okay. Times the velocity of the ball initially. 7.6 m/s. Okay, plus the mass of us, 65.8 kg. And our initial velocity well, that's just zero. Okay, so this term is going to go to zero as well. Then on the right hand side we have the mass of the ball again, .55 kg Times the velocity of the ball at the end -11.3. Okay, remember momentum is a vector. So in this momentum equation we're using velocity, velocity is also a vector direction matters, so we need to include the negative to indicate that we're going in the opposite direction. Alright? And then the mass of us, 65.8 kg times V two F. That quantity that we're looking for. Alright, so let's simplify that. Okay, and what we're gonna get we're gonna get 4. kilogram meters per second. On the left hand side. On on the right hand side, we're going to have -6.215. Again, the unit is going to be kilogram meter per second. Okay, so we're multiplying kilogram times meter per second. So, a new unit is kilogram meters per second and then we have 65.8 kg times V two. Alright, so we have the same units here, we can add and subtract no problems. We're going to move this value over and we're going to have 10.395 on the left hand side, kg meters per second, still on the right hand side, 65.8 kg times V two F. Alright, so now we're gonna divide and what's going to happen is the unit of kilogram is gonna cancel. Okay, we're left with V two F is going to be equal to 0.158 m per per second. Okay, Alright, so this is our velocity and it's positive. So that's telling us that after we deflect the ball, we're going to be moving backwards, That makes sense. We're on a slippery surface. So the ball is going to come towards us collide with us, we're going to bounce it away and that ball is going to push us a little bit backwards. Alright, so now to wrap up the question, the question is asking for speed. Okay, so the speed is actually going to be we can call it V two F without the arrow and that's what's going to be the absolute value of the velocity. In this case it's going to be the same. 0.158 m per second. Okay, so that's the answer we were looking for and that's going to correspond with solution E. Alright. Thanks for watching. I hope that helped guys see you in the next video.

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