Question

A bullet moving with a velocity $u$ passes through a block at rest and free to move. The two are of equal mass. After passing through the block, the velocity of the emerging bullet is $fu$. Its velocity relative to the block is :

• A. $fu$
• B. $(1-f)u$
• C. $(2f-1)u$
• D. $(2-f)u$

Answer 1

The correct option is C $(2f-1)u$

Initial momentum $=$ final momentum

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

But $u_1=u,u_2=0,v_1=fu$

$mu+m\left(0\right)=mfu+m{v}_2$

$v_2=(1-f)u$

Relative Velocity $=|v_1-v_2|$

Relative Velocity $=|fu-(1-f)u|$

Relative Velocity $=(2f-1)u$