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Two cars collide at an intersection. Car $A$, with a mass of 2000 kg, is going from west to east, while car $B$, of mass 1500 kg, is going from north to south at 15 m/s. As a result, the two cars become enmeshed and move as one. As an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 65$^\circ$ south of east from the point of impact. (a) How fast were the enmeshed cars moving just after the collision? (b) How fast was car $A$ going just before the collision?

(a) $P_{1 x}=P_{2 x}$ gives $(1500 \mathrm{kg})(15 \mathrm{m} / \mathrm{s})=(3500 \mathrm{kg}) v_{2} \sin 65^{\circ}$ and $v_{2}=7.1 \mathrm{m} / \mathrm{s}$(b) $P_{1 y}=P_{2 y}$ gives $(2000 \mathrm{kg}) v_{A 1}=(3500 \mathrm{kg}) v_{2} \cos 65^{\circ} .$ And then using $v_{2}=7.1 \mathrm{m} / \mathrm{s},$ we have$v_{A 1}=5.2 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

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This is an interesting problem. It's a collision problems so well given well given on intersection that's running west east on one direction. And then, you know it's running, you know, not self in another direction. We have two cars. Car, Eh? So this is what happens before. So car A with the mass off given the Marcel's car, eh? It happens to be, um so you know, we're gonna have to get the mass of this. So the mass ofthe car A happens to be two thousand kilograms. This is two thousand kilograms muscle car, and it's moving in the X direction. So initial the velocity off here, the ex direction happens to be, you know, we don't know what that initial velocities in the ex direction. We do know that the initial lost in the white direction his zero meters per second because it's moving from West Teo east. So this is kind of like in the postive direction. You want to think of it that way. Then we have another car, will given cobby that's moving. So car is moving west to east and then Kirby Mom is moving from north to sup. It's moving from not this out so you can have conventions where not South can be negative. For example, if you want Andi, that's just fine. You know, we could say, If you're going downwards, that's negative. If you're going to the right, that's positive. You're going upwards. That's positive. If you're going to the left, that's negative. Those are conventions you can use on DH, then the muscle. He happens to be given us fifteen hundred kilograms. The initial velocity off B in the ex direction happens to be zero because it's not moving in the extra action. It's moving not south, and then the final velocity, or rather, the initial velocity off being the wide direction. That's kind of what's given. Mom happens to be, if you if you say downwards his negative. So that's going to be not South negative, fifteen meters per second. That's the information we've given before, and then after afterwards, what's gonna happen is the two cars will collide at the intersection, and B, this is a this is B and then they're going to move a certain direction. So this is sixty five degrees. This is east. This is west. This is not who's so so they'LL have a final Kamen Velocity, which you call the final and that vi final. Kamen Velocity has component factors, so the downward downward component vector would be the final sign of sixty five. As you can see, because it's opposite the angle sixty five and then Cem VI final in the X direction will be the final. Of course, I knw of sixty five. So those are some things we're given and we want to find out in part a. What's the final? What's this Final velocity combined velocity after they collide and then we also want to find out. But the initial velocity in the ex direction for a okay, velocity off he just before collusion assume we have limited friction and were using the laws ofthe conservation of momentum. So in party, the initial momentum because to the final momentum. And we want to find the initial velocity. So initial momentum in the acts will start with the ex direction. Use the ex direction to find the final velocity. So the initial momentum in the X it would be the Marcel's eh times the initial lost you, eh? In the X plus the Marcel's B times the initial velocity of be in the X. When they stick together, their masses combined as a son and they have a common velocity in the X, which happens to be the final sign of sixty five. This is this is what we're looking for. The V finer. So you could see the VI final is equivalent to the Marcel's, eh? Velocity of pay. The ex plus Marcel's b lost your being the ex all over mass of a plus Must will be a sign of sixty five is going to be sign of sixty five with plug in the numbers Get to see that the muscles, eh? Going back is two thousand kilograms two thousand kilograms and then the velocity of pain The X is Come on You were using lost you so massive Massive Hey, um maybe we should use why for this one. So two thousand kilograms? Ah, mussels. I'm sorry Way have to do in the white direction not the ex direction because we don't have the initial blast e both home. We don't have the initial blast. You off off, B No, we don't have the initial velocity of a couldn't see. We don't have this one. So we have to go back and do it in the white direction. So was saying initial velocity in the wind direction. So this is not expert. We are going to do. Why then? And of course, it makes sense for the y to be signed. You could see that so that why sign? That's That's what I'm going to use. We just don't have the sub scripts for for why, right here to change that. So initial velocity off in the y. So this is not the ex direction, but this is the wind direction. Just recall. So this is why this is why this is sign of sixty five on then Also we have initial blast. Why initial velocity? Why will be so This is two thousand kilogram initial last year off in the white direction is zero meters per second showed. You know, that's that's how we're doing this one. And then we added to the mass off B which happens to be fifteen hundred kilograms and forget the killer blond right there. Fifteen hundred kilograms times the initial velocity off be in the white direction and that happens to be negative fifteen meters per second and the negative sign touches houses just come in the direction. You know what what direction is? And then the muscles, eh? Two thousand kilograms, plus the muscle B, which is no, which is fifteen hundred kilograms. Okay, men, Time sign of sixty five. And so something you want to know is that Oh, when you plug in, the numbers will be able to get the of the final, which happens to be seventy. We're not seventy, but seven seven point one meters per second. This is the final seven point one meters per second. Um, sign this case. The reason why in fact, we don't even have to use the minus of this minus. We don't have to use this minus right here. You were comfortable. We just know the direction. Let's think about the direction East west, not south. So you don't have to use those sciences We've done right. Who left before eso coming back to see that the final velocity is seven point one meters per second and then the second part of the problem Oh, you want to find I want to find the initial velocity if you call it this one right here. Initial velocity of a That's what we want to find that one V eh? I x So we want to find the initial velocity off a which we're calling the A i X. So we're going to use the ex direction formula Now We're dealing with ex direction and had so little saying the initial momentum in the X here used initial momentum in the white direction just to be clear about that now it was saying initial momentum in the ex direction because to the final momentum in the ex direction, initial momentum in the ex direction is muscle times, velocity of a initial velocity of paying the ex direction. Plus must be time's initial velocity of B in the X direction. When they stick together, we have Marcel's hate plus must be But now we're dealing with the ex direction on this side. You see, we had I had lost why and then this one was was our If you go back to the diagram the final sign sixty five you know that you could call that V off f y And then this one is a vey off f of X. So we're going to use V o F of X, which is the call sign off sixty five. The call sign of sixty five. I already have V from the previous problem. Would you call the final right here? That's Avi file. Eso won good ship. Want to solve for the initial velocity of aid X direction No one was simplified. That problem. We get initial velocity of pained extractions. Emmy plus M b. The final co signed sixty five and then minus empty, be initial in the X all over the muscle. He plug in the numbers Marcel Hayes two thousand kilograms. So we have two thousand kilogrammes times. We'LL run the plus one thousand five hundred kilograms times seven point one meters second co sign sixty five minus muscle B is, um one thousand five hundred kilograms. But remember, the initial velocity of being the ex direction happens to be zero. So that's just means that we're not gonna have any momentum. In that instance, we have to divide all that bye the muscle a day, which happens to be two thousand kilograms. When you simplify that problem, you end up getting but the last e to be five point two five meters per second So this is the last year of a the ex direction. Come happens to be five point two five meters per second. Initial velocity of ain't extraction Hope you enjoy the problem. We had to find the VI final Blast e when they meet in the intersection and they collide. And that's number we had. And then we also had to find the initial last year a just before the collision. Okay, So if you have any questions, feel free to send them my way and have a wonderful day. Okay, Thanks. Bye.

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