Question

A cannon of mass $m_1$ fires a shell of mass $m_2$ with speed $v_0$ relative to the barrel which is inclined at an angle $\alpha$ with horizontal . Find the recoil speed of cannon if it is placed on ice.

• A. $\frac{m_2{v}_0\cos \alpha }{(m_1+m_2)}$
• B. $\frac{m_1{v}_0\sin \alpha }{(m_1+m_2)}$
• C. $\frac{m_2{v}_0\cos \alpha }{(m_1-m_2)}$
• D. $\frac{m_1{v}_0\sin \alpha }{(m_1-m_2)}$

Answer 1

The correct option is A $\frac{m_2{v}_0\cos \alpha }{(m_1+m_2)}$

Since the cannon is placed on ice, the surface can be considered frictionless. The situation can be shown as below

Let the recoil speed of cannon be $v$ w.r.t ground
velocity of the shell w.r.t ground $=v_0\cos \alpha -v$
Applying momentum conservation in horizontal direction, we have
$0=m_2(v_0\cos \alpha -v)-m_{1}v$
$\Rightarrow v=\frac{m_2{v}_0\cos \alpha }{(m_1+m_2)}$