Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. M 3M M 3M Before After (a) (b) v A cord holding them together is burned, after which the block of mass 3M moves to the right with a speed of 1.3 m/s. What is the speed of the block of mass M

-3.9 m/s

Explanation:

Given that

Initial velocity, u of both bodies = 0

Initial momentum of the bodies = 0

Final velocity, v of the 3M block = 1.3 m/s

Mass M of the block A = M

Mass m of the block B = 3M

To solve this question, we would have to use the law of conservation of momentum. The law states that in any system, momentum is always conserved. Thus, initial momentum = final momentum. Mathematically, we have

M * V(a) + 3M * V(b) = 0

The velocity of the block 3M block is V(b) has been given to be 1.3 m/s, so then

M.V(a) = - 3M * 1.3

V(a) = -3.9M/M

V(a) = -3.9 m/s

no. dot product   =0 when vecs at right angles