In this problem. We have a person on a boat walking from end to end on. We're told how much the boat moves relative to the water that it's in and were asked to determine the first the length of the boat and then also how much the center of mass of the system moves and were given. The mass of the boat is 130 kg, and the mass of our person is 80 kg and the boat moves 0.8 m. Eso what we'll do here is will use conservation of momentum, uh, to say that our system since we're told that our the system conserves momentum. So the center of mass of our system does not change eso when the boat moves by 0.8 m are center of mass of relative to the boat has to move by an equivalent 0.8 m. We could look at this from a point of view of velocities and distances, but it will be simpler just to look at it from the center of mass perspective. So our part a, uh is asking us what is the length of the boat. And so we're looking at Here are distance. So our boat, we're assuming our boat is uniform. So this 130 um, kilograms is acting at a distance of El over to. And so what we'll do, we'll say that are X. So we start with our center of mass at X initial, and we finish with our senator mass at X Final, where we're measuring relative to the boat on So we can say that X final minus R X initial equals this 0.8 since our center of mass is going to remain in the same position. So as our person is walking to the right, our boat has to move equivalently to the left. Right. Okay, so let's find our to, uh, positions for center of mass. So x initial and x one. Okay. Initially, our center mass is going to be 3100 and 30. So we're starting at the left end of the boat is zero. So we have 130 times l over to over 130 plus 80 and we can That will give us a 13 over 42 help, and then finally, Rx final. It's going to be again measuring from the left end of the boat relative to the boat, the left handed zero. So our center of mass is going to be 80 or person has moved to the right edge of the boat 80 times l and plus our mass of the boat acting at its center l A. To and divided by 1 30 plus 80. And that will give us 100 45 over 210 out. So relative to the boat, the center of Mass has moved by this distance. And then the boat has moved by this distance 0.8. So doing our location here 145 210 hour minus 13/42 eloquent zero 0.8. And if we just saw that for l get our AL equals to 2.1 meters and then our part B asked, asks us what happens to the center of mass of the system, right? And it, uh, it doesn't move. So what we can see what would happen here is are so are yeah. So we saw our center of math. Our boat moves one way our person moves this way on our boat. It is moving in the other direction, but the center of mass of the system is going to remain in the same position. Right? So if we're are looking from an outside perspective, right. So our boat, our boat moved 0.8 m to the left and our center of mass relative to the boat moved that much distance to the right.