Question

A bullet of mass m is moving with velocity u penetrates into a block upto thickness d,if the block is fixed.now if block is free to move on smooth horizontal surface and bullet is fired into it symmetrically with same velocity u ,it penetrates upto thickness d'.assume resistance force due to block on bullet in both the cases is same. find ratio d/d' if m=M(mass of block).

Answer 1

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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:

this is a little complicated to find.

Explanation: