Mr. Verma (50kg) and Mr. Mathur (60kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting frictioin with water how far does the boat move on the water during the process?

Explanation

Here the system is Mr. Verma + Mr. Mathur + boat. Net force on this system is in horizontal direction is zero and initially the centre of mass of the system is at rest. Therefore the C.O.M does not move in horizontal direction. Let x be the displacement of the boat. Then We can use the concept
`m_(1)x_(1)=m_(v)x_(v)+m_(M)X_(m)`
`40xx x=50xx(2-x)-60(2+x)`
`40x=100-50x-120-60x`
`150x=-20`
`x=-2/15`m

`x~~13` cm (right wards)