Okay for this question. We're asked to analyse two cars. Well, they call them cars are sliding objects on this frictionless surface. They asked us questions before and after a collision. So, for the sake of um, and easy and clear and to be clear, I'm going to label this first part A and the second Kirby. And the problem tells us that Car A Has a massive 0.15 kg and is moving 1.2 m/s to the right. Car B Has a massive .25 kg and is not moving. All right, so let's look at part A first for A wants us to find the net momentum of this system before this collision. So to do that, we can say that our net momentum is equal to the momentum of car A plus the momentum of Kirby, which we can break down further into Minister A times velocity of A plus must be times the last thing to be. We know that velocity B is equal to zero because it is not moving. And so that will make Carvey has zero momentum. So are all of our momentum comes from Car A Will be 0.15 kg Times 1.2 it is per second. So in that momentum, if we put that into our calculators will give us The total that momentum of 0.18 several grams times meters per second. Okay, now for part B, they want us to um identify what our momentum after our collision must be. And then they ask us why now our momentum is always conserved in these collisions. And so if our momentum of our entire system was 0.18 kg tens meters per second, then after a collision, our net momentum must be conserved. So it must be 0.18 kilograms times meters per second. That must be because the momentum, it's actually right now is concert. So that means we're not going to lose momentum or danish now for currency. They ask us to use those two answers and to come up with what our velocity must be. So we have been appearing our picture after a collision which is represented by the squiggling line. These masses are now stuck together, mess A. Msb. They want us to find what that velocity is going to be. So adding the two masses together. Okay, we can find our total mass now of our new car, as we could say, Which would just be 0.15 Plus 0.25. Okay, so let's use that to calculate the velocity. You know where momentum is equal to mass times velocity. And now our math here is going to be our total mass. So it's going to be mass A plus, mass B. And all of that time. The final velocity. Now the momentum we are given And that must be 0.18 since it's concerned. So let's put some numbers into that equation. 0.18 kill advance tens meters per second is equal to Math A. was 0.15 kilograms. Mass be with 0.25 kg and then we have that final velocity. Mm So let's work with our friend. This is 1st 0.15 Plus 0.25 will give us 0.4 0.4 kg Times the frame of velocity is equal to 0.18 kilograms meters per second. Now, if we divide both sides as you're going forward, general grams we get that our final velocity Is equal to 0.45 meters per second. We can know that it's needed per second because kilograms will cancel out on that side of our equation. So the answer to part C 0.45 m/s. Now, it's good to note that our velocity is going to greatly slow down because our math has increased. Okay, so for party they want us to ask or they want us to identify whether this kinetic energy is concerned. The best way to look at this is to look before and after. Kinetic energy Is equal to 1/2 some squared Now, since Kirby has zero Kinetic energy Where it has zero velocity, They will have zero kinetic energy. So the kinetic energy is ultra um a Which is going to be 1/2 0.15 kg. Change its velocity of 1.2 m/s, correct? So if we plug it into our calculator, we can get a number and analyze. I'll take 1/2 times 0.15 Times The Square of one Point. And we should get an answer. 0.108 jewels Now for our kinetic energy. After we've increased the mass and decrease the speed, which hard hard to tell. But we can calculate it. There will be 1/2 Now. Our new mass of A&B 0.4 kg and a new velocity, which we just calculated was 0.45 m person. Well, we will square that and we can plug that into Our new kinetic interviews for 1/2 Times 0.4 Times The Square of 0.45. And we get that our new kinetic energy is 0.0405 jules. So we can see from these two comparing kinetic energy before and after that are kinetic energy is not concerned. That is a good thing to remember about our collision. Or kinetic energy will not be conserved within this collision will lose, energy is either sound or heat, um but our momentum will always be concerned.