Question

A cannon mounted on the back of the ship fires a 50 kg cannonball in the horizontal direction at a speed of 150 m/s. If the cannon and the ship to which it is firmly attached have a mass of 4000 kg and are initially at rest , what is the speed of the ship just after shooting the cannon? Ignore air resistance.

Answer 1

Given:

A cannonball of 50kg mass is fired with a speed of 150m/s from a ship of 4000kg which is at rest.

To Find:

The speed at which the ship will move just after shooting.

Solution:

Mass of the cannonball, $m_1=50kg$

Mass of the ship, $m_2=4000kg$

The speed with which the cannonball was fired, $v_1=150m/s$

Let the speed of the ship after firing be $v_2$

Here in this problem, initially, both the ship and the cannonball were at rest.

So initial momentum of the system $=0$.

As no external force is applied to the system, according to the law of conservation of linear momentum, the momentum of the system must remain constant, i.e. $0$ in this case,

⇒ $m_1v_1+m_2v_2=0$

⇒ $50(150)+4000(v_2)=0$

⇒ $4000v_2=-7500$

⇒ $v_2=-\frac{7500}{4000}$

⇒ $v_2=-1.875m/s$

Hence, the ship will move with a speed of 1.875m/s opposite the cannonball direction.