A 1000 kg cart is rolling to the right at 5.0 m/s . A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of 10 m/s relative to the cart?

Video transcript

Hey everyone. So this problem is dealing with conservation of momentum. Let's see what it's asking us. A truck having a mass of 500 kg is traveling toward the east with a speed of eight m per second. A fiber optic cable cable roll weighing 120 kg is placed on the truck. The cable roll suddenly rolls towards the back end of the truck with a speed of 1.5 m per second relative to the truck. Calculate the new speed of the truck. Our multiple choice answers here are a 7. m per second. B 8.29 m per second. C 9.29 m per second or d 7.92 m per second. So the key to this problem is going to be recalling our conservation of momentum which says that our initial momentum is equal to our final moment. And in turn, momentum is given by mass multiplied by velocity. So when we look at both of these scenarios, initially, when the cable is in the truck moving together, and then finally, when the cable has kind of sprung free, sprung free in the bed of the truck and rolls to the back of the truck. So our initial conditions, our initial scenario is going to be the mass of the truck multiplied by the initial speed of the track plus the mass of the cable multiplied by the initial speed of the cable. And that will equal that final scenario. We have the mass of the truck multiplied by the speed of the truck, which is the value we're solving this problem for plus the mass of the cable multiplied by the final speed of the table. So when we look at each of these terms, one by one, given the information from the problem we have, we know the mass of the truck is 500 kg. The initial speed of the truck is eight m per second. The mask, the cable is given as 100 and 20 kg. And the initial speed of the cable, initially, the cable is in the bed of the truck. So it will be traveling at the same speed as the truck. So that is also eight m per second. We, when we look at the right hand side of the equation, we know we're solving for this final speed of the truck. And so the last variable in this problem is the final speed of the cable. And from the problem, it tells us that it's rolling towards the back of the truck at a speed of 1.5 m per second. Relative to the speed of the truck. So that will be the speed of the truck minus 1.5 m per second because it's moving in the direction opposite that of the truck. And so from here, we actually have everything we need to plug into this equation and solve for the final speed of the truck. So we'll have 500 kg multiplied by eight m per second plus 120 kg. Multiplied by eight meters per second equals kg. Multiplied by V T F plus 120 kg, multiplied by BT F minus 1.5 m per second. When we plug all of this in to our calculator, the left-hand side of the equation simplifies to sorry, 4960 kg meters per second. And that's equal to 500 kg multiplied by V T F plus 120 kg multiplied by V T F minus 180 kg meters per second. So we'll add 180 kilogram meters per second to both sides. We get 5000, 140 kilogram meters per second is equal to 620 kg multiplied by V T F. And finally can solve for BT F which equals 8.29 m per second. And so that is the final answer for this problem. And when we look at our multiple choice solutions, it aligns with answer choice B So that's all we have for this one. We'll see you in the next video.