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A pirate is sitting on a small boat with a loaded cannon. In desperate need of food, he fires the cannon at an Albatross bird sitting in the water (he misses). The cannon ball has a mass of 49 kg and leaves the cannon with a velocity of 134 m/s. If the pirate and everything else on the boat have a mass of 356 kg, what is their velocity right after the cannonball is fired?



Answer :

Given data:

* The mass of the cannonball is m_1 = 49 kg.

* The initial velocity of the cannonball is u_1 = 0 m/s.

* The final velocity of the cannonball is v_1 = 134 m/s.

* The mass of the boat and pirate is m_2 = 356 kg.

* The initial velocity of the boat and pirate is u_2 = 0 m/s.

Solution:

According to the law of conservation of momentum, the net momentum of the system in the initial state is equal to the net momentum of the system in the final state.

Thus,

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/tex]

Substituting the known values,

[tex]\begin{gathered} 49\times0+356\times0=49\times134+356v_2 \\ 0=6566+356v_2 \\ 356v_2=-6566 \\ v_2=-\frac{6566}{356} \end{gathered}[/tex]

By simplifying,

[tex]v_2=-18.44\text{ m/s}[/tex]

Here, the negative sign indicates the motion of the boat and pirate is opposite to the direction of the cannonball.

Thus, the velocity of the boat and pirate after the cannonball fired is -18.44 meters per second.

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