A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?

Video transcript

Hey, everyone in this problem, we have a science fiction movie where a policeman is going to stop a thief moving on a motorcycle at a speed of 18 m per second due east by shooting a two kg sticky ball at it. The combined mass of a thief in his motorbike is 350 kilometers. And we're asked to calculate the ball's velocity. We're given four answer choices here. Option A and B both have a speed of 324 m per second. They just change in which direction it is moving. Same with option C and D. They both have a speed of 3150 m per second but have a different direction. No, you can think of this two kg sticky ball that's gonna hit this motorcycle as a collision problem. OK. We have a collision. We want to think about the conservation of momentum. So we know that our initial momentum P knot is going to be equal to our final momentum P F. OK. That's our conservation of momentum. Now we have two objects in our system. We have the motorcycle and when I say motorcycle I mean, both the thief and the motorcycle combined and then we have our sticky ball. So we have to consider the momentum of both of those. So we have P not M the initial momentum of the motorcycle plus thief, A plus peanut B, the initial momentum of that ball. And that's gonna equal P F M plus P F B. OK. Those same um subscripts M and B representing the motorcycle and the ball respectively. And we're in the final case after the collision. Now let's start with direction before we get into substituting our values. We're told that the thief in the motorcycle are moving to East. OK. So East is to the right and we're gonna take that as our positive direction. No, we have momentum as a vector. OK? That means that the direction matters and that is why we needed to pick a positive direction. And because we need to include information about that direction in our momentum. Now recall that momentum is mass multiplied by velocity. So for each of these terms, we have the corresponding mass multiplied by the corresponding velocity M M V R M plus M B V, not B is equal to M M V F M plus M B V F B. All right. Now, let's simplify the right hand side a little bit. OK? We're gonna leave the left hand side alone on the right hand side. This is a sticky ball. So once it gets thrown and hits the motorcycle, it's going to stick to it and they're gonna move all together. Ok. So that means that the speed after the collision of the ball is gonna be the same as a motorcycle. Ok. So we're gonna have the total mass M M plus M B multiplied by the final velocity. We're just gonna call it V F of all three of those things, the thief, the motorcycle and that sticky ball because they're stuck together, ok? And they're moving with the same speed. Now we know that the policeman wants to stop the thief and so that final speed is actually gonna be zero, ok? The sticky ball is gonna be thrown, it's gonna hit the motorcycle, it's gonna bring it to a rest so that the motorcycle, the thief and the ball that is stuck to the motorcycle are not moving. So that final speed V F is zero, which means that the entire right hand side is zero. Now substituting any other values, we have the mass of a motorcycle and thief is 350 kg multiplied by the initial speed of 18 m per second plus the mass of the ball two kg multiplied by the initial velocity of that ball and all of this is equal to zero. Now, we want to solve for that initial velocity of the ball before the collision. Now we can move this kg multiplied by 18 m per second. To the right hand side that gives us negative 6300 kilogram meter per second. And then we're gonna divide by two kg to isolate V not B. So the unit of kilogram will divide out, we get 6300 divided by two which gives us a final velocity or sorry, a an initial velocity of this ball of negative 3150 meters per second. All right. So the speed, the final speed, if we look at just the magnitude of this velocity is 3150 m per second. So we know we're looking at option either C or D, we need to interpret the direction. Now we got a negative value. Remember at the beginning, we chose the east to the right to be our positive direction. If we have a negative value, that move means we're moving in the opposite direction. And so this ball is going to be moving west. And so the correct answer here is that the ball should be shot west at 3150 m per second. And that makes sense. If we want to stop this motorcycle, we should be shooting the ball in the direction opposite of their motion. So we have answer choice. D thanks everyone for watching. I hope this video helped see you in the next one.