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. a cord holding them together is burned, after which the block of mass 3m moves to the right with a speed of 2.4 m/s. what is the speed of the block of mass m?

The speed of the mass M is 7.2 meters per second

Explanation:

In this case because there aren't external forces on the system blocks-spring and the spring is light we should apply the conservation of linear momentum (P) that states:

(1)

Momentum is mass (m) times velocity (v) ( (2)) and Initial momentum is zero because the blocks are released form rest, so (1) is:

Using (2) on (1):

(3)

It's important to note that momentum and velocity are vector quantities so we should take care of directions, assuming right direction as positive, velocity of 3M mass is positive, and velocity of M mass is negative, (3) is:

solving for

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