Question

A wheeled cannon of 200 kg fires a cannonball of 1 kg horizontally. The ball leaves the cannon travelling at 200 m/s. At what speed does the cannon recoil?

• A. 0 m/s
• B. 1 m/s
• C. 2 m/s
• D. 4 m/s

Answer 1

The correct option is B 1 m/s

The initial momentum of the system,
$p_i$ = 0 (as the cannon and the ball are stationary)

Finally, the ball is moving with a velocity of 200 m/s.
Let the recoil velocity of the cannon be v.
Final momentum of the system,
$p_f$ = 1 x 200 + 200 x v = 200 + 200 v

During the cannonball’s launch, the net external force on the system is zero. So, the momentum of the system is conserved.
$p_i$ = $p_f$
0 = 200 + 200 v ⇒ v = - 1 m/s
The negative sign implies that the cannon recoils in the direction opposite to the velocity of the ball with a speed of 1 m/s.