Question

A 1385 kg cannon containing a 58.5 kg cannon ball is on wheels. The cannon fires the cannon ball, giving it a velocity of 49.8 m/s north. What is the initial velocity of the cannon the instant after it fires the cannon ball?

Answer 1

Initially, the total linear momentum is zero. The final total linear momentum will also be zero. I have arbitrarily assigned a positive direction for north for the final velocity of the cannon ball. When you solve for the final velocity of the cannon you will get a negative number, indicating that it moves in the opposite direction. This makes sense because the cannon recoils.\[\color{green}{\begin{align*} m_1\vec{v_1}^{'}+ m_2 \vec{v_2}^{'} &= 0 \\ (1\,385~\text{kg})(\vec{v_1}^{'}) + (58.5~\text{kg})(+49.8~\text{m/s}) &= 0\end{align*} } \]

Answer 2

yes i'm right xD
thanks!