Question

A bullet of mass m moving with a velocity u passes through a wooden block of mass M=nm The block is resting on a smooth horizontal floor after passing through the block the velocity of the bullet is v find its velocity relative to the block

Answer 1

Let's consider, our system to be the bullet as well as the block.
Since, there is no other external force acting on the system , (gravitational forces can be ignored since the motion is to be considered only in the horizontal direction)

Now,
Initial momentum of the system = mu

Let the velocity of the block after collision occurs and the bullet again comes out of the block be v1

So, Final momentum = Mv1 + mv

Initial momentum = Final momentum
So,

mu = nmv1 + mv
Therefore,
v1 = (u-v)/n

So, the velocity of the block will be (u-v)/n

And , the relative velocity of the bullet with respect to block will be
v-v1 = v-(u-v)/n
= nv+v-u/n = ((n+1)v-u)/n

Hope this helps you !

Answer 2

Answer:

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