Question

A hockey puck of mass $m$ is initially at rest on a frictionless ice rink. A player hits the puck, imparting an impulse of $J$. If the puck then collides with another stationary object of mass $M$ and sticks to it, calculate the final velocity of the two-body system.

• A. $\frac{J}{m}$
• B. $\frac{J}{M}$
• C. $\frac{J}{m+M}$
• D. $\frac{m+M}{J}$
• E. $\frac{M}{J}$

Answer 1

The correct option is C $\frac{J}{m+M}$

As we know , impulse = change in momentum

here $J=m{v}_2-m{v}_1$

But puck is initially at rest so $v_1=0$

So $J=m{v}_2=p$ this impulse or momentum is imparted to puck.

,

$p$ is the momentum of puck before collision

Now , by linear momentum conservation law

Momentum before collision=Momentum after collision

$m{v}_2=(m+M)v$

or $J=(m+M)v$

or $v=\frac{J}{(m+M)}$ (final velocity)