Two trucks of mass M each are moving in opposite direction on adjacent parallel tracks with same velocity u. One is carrying potatoes and other is carrying onions, bag of potatoes has a mass m1 and bag of onions has a mass m2 (included in the mass of truck M). When trucks get close to each other while passing, the drivers exchange a bag with the other one by throwing the other one. Find the final velocities of the trucks after exchange of the bags.
Here at the time of exchange of bags, momentum in the direction of individual motion remains conserved. The situation is shown in figure.
When driver of first truck carrying potatoes, throws a bag of mass m, in a direction perpendicular to the motion direction, towards the other truck, as shown in figure. During throw the bag has a velocity u in the direction of motion of the first truck. Similarly, when the second truck driver throws the onion bag conserve momentum for both the trucks independently as
First truck carrying potatoes
On solving, velocity of first truck after exchange is v1=Mu−m1u−m2uM−m1+m2
Second truck carrying onions
On solving, velocity of first truck after exchange is v2=Mu−m1u−m2uM−m2+m1