The track shown in figure (9-E16) is frictionless. The block B of mass 2m is lying at rest and the block A of mass m is pushed along the track with some speed. The collision between A and B is perfectly elastic. With what velocity should the block A be started to get the sleeping man awakened?

_{Given that the block B has mass 2m and the block A has mass m.}

_{Let the velocity of A is u}at which it should started,

_{Let the final velocity when reaching at B becomes v1},

Since, by work energy principle

________________ (1)

When the block B reached at the upper man’s head, the velocity of B is just zero.

For block B, applying work energy principle

Therefore,

Therefore, before collision the initial velocity of block A is v₁ and initial velocity of block B is 0.

After collision the final velocity of block A is v (say) and final velocity of block B is

Since it is an elastic collision the momentum and kinetic energy should be conserved.

Therefore,

___________ (1b)

By law of conservation of energy

________________ (2)

Dividing equation (1) by (2)

_____________ (3)

Adding (1b) and (3)

But

So With velocity should the block A be started to get the sleeping man awakened.