 So, in this problem it is given that there are two people standing at the two extremes of a boat which is on the surface of any river or pond and the boat is of 40 kgs mass. The person one is of 50 kgs mass and the another person is of 60 kgs mass. Now the question is that they come together after some time at the center of the boat. Now we have to find out how much will be the shift in the boat or how much will the boat move. Now the underlying concept clearly in this question is center of mass and we know that if there is no external force acting on the system then the center of mass of the system stays at the same point. Now if we consider the two people M1, M2 and M3 boat that is as a system then there is no external force in the horizontal direction since it is also given that there is no friction on the surface of the water and that is between the surface of the boat and the surface of the water. So that means there is no external force acting on the system so hence in the horizontal direction the center of mass of the system will stay wherever it is. So using that concept we will solve this problem so how to start or how to frame the solution. So basically we will be using the underlying concept as we studied that the center of mass will stay at the same location whatever happens to the individual elements of the system in the horizontal direction. Now let us assume that the coordinate system with reference to which we are going to find out center of mass is attached to the center of mass of the system itself that means if let's say this point was the center of mass now the question many people or many students ask how do I know that the center of mass will be on the right side of the center of the boat which is pretty obvious this mass is 50 kgs and this is 60 kgs so we can you know analyze it critically let us say that this was 50 kgs also so M1 and M2 is 50 kg and M3 is 40 kgs so clearly the center of mass will be at exactly at this this line this line this line but since M2 is 60 kg that means in a way you can think of that you are adding 10 kg extra on the right hand side that means the center of mass will shift towards the right so let us say the center of mass is towards the right of the center of mass of the boat so at this location oh let's say and now let us say that the person standing on the right is at x2 coordinate x2 coordinate from the center of mass of the system and center standing also the person standing on the left is x1 meters away from the center of mass and obviously now the boat center of mass will be x3 meters away from the system center of mass once that is done then what can we say so x1 is position of M1 and how much that will be so if you see the total length of the boat is 4 meters so from the center of mass of the boat to the extreme point will be 2 meters and from the center of mass of the system the person M1 is 2 plus x3 meters away right so hence his x coordinate M1's x coordinate will be 2 plus x3 so 2 is this much this much is 2 and then this much is x3 so 2 plus x3 similarly x coordinate of M2 will be 2 minus x3 meters and x3 is the position of the center of mass of the boat so by the definition of center of mass we know that xcm that means center of masses x coordinate this xcm is the center of mass of the three body system what are the three bodies M1 M2 and the boat so according to that summation mi xi some divided by summation mi and that must be equal to zero so where i is varying from 1 to 3 because there are three three three individual components in the system so similarly in the denominator also I have not shown the the limits but we know what it means that means if I do the numerator it is 50 into negative 2 plus x3 so this was 50 into the distance plus 60 into this distance that is 2 minus x3 and plus 40 times negative x3 why am I taking negative because both M1 and M3 are on the on the negative x coordinate negative x side of the center of mass so this is the numerator divided by the total mass of the system that is 50 plus 60 plus 40 that must be equal to zero why because we have considered that the center of mass or we have considered that the the coordinate system is located at the center of mass of the system so if you solve this you will get if you solve this thing you will get x3 is equal to 2 by 15 meters 2 by 15 meters now if you see 2 by 15 meters is when the people were at the two extremes and this is the this is x3 is 2 by 15 meters that is it is 2 by 15 meters away from the center of mass of the system what is 2 by 15 meters away the board center of mass is 2 by 15 meters away from the center mass of the system now if in the second case these two people come together or and it is given that these two people center are moving towards the center so that means after that after them they have moved they have come to the center of the board and the center of the board itself is at the center of the board in the same location that is that means the entire mass you can think of now is concentrated at the center of the board center of the board is it it now what does it mean this means that the now the center of mass has is now in the second case in the case number 2 case number 2 when all of them have come together the center of mass is located at the center of the board that means what would have happened what would have happened to for the center of mass of this system that means this is this was the original position of the center of mass where here this is the original position of center of mass center of mass is here now it is so happening that all of them are coming together and now the new center of mass is exactly at the center of the boat because both the people as well as the boat itself you know both the people are exactly on top of the center of mass of the boat that means that means what a new center of mass must lie here itself because you can think of all the masses are concentrated at this position but we know that there is no external force that means center of mass must not change its direction or position then what will happen that means that this point this point P let's say must have traveled to this point O so that the center of mass is maintained at the same location that means the boat must shift by X3 distance in the in the second case so that the center of mass is still at that location so hence what is the answer the answer is X3 meters towards the right the boat will shift so that the center of mass is maintained at the same location hence the answer is 2 by 15 meters towards the right