Question

A cannon of mass $1000kg$ can fire a bolt of $20kg$ with a muzzle velocity of $300m{s}^{-1}$. If the cannon is free to move, the backward velocity of cannon after the bolt is fired will be:

• A. $6m{s}^{-1}$
• B. $9m{s}^{-1}$
• C. $7m{s}^{-1}$
• D. $8m{s}^{-1}$

Answer 1

The correct option is A

$6m{s}^{-1}$

Given, muzzle velocity of the bolt, $v_m=300$,
mass of cannon, $m_c=1000kg$ and
mass of bolt, $m_b=20kg$.
Let the velocity of the cannon after firing the bolt be $-v$. (negative sign indicates that the cannon will move backward).

From the law of conservation of momentum, the total momentum of the cannon and the bolt before firing should be equal to the total momentum of cannon and bolt after firing.
Hence, initial momentum = final momentum;
$0=1000\times (-v)+20\times \left(300\right)$ (since, total initial momentum is zero as both bodies were at rest before firing).
$\Rightarrow 0=-1000v+6000$
$\Rightarrow 1000v=6000$
$\Rightarrow v=6m{s}^{-1}$
Hence, the backward velocity of cannon will be $6m{s}^{-1}$.