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 - with horizontal- Find the recoil speed of cannon if it is placed on ice-A- m1 v0sin-m1-m2B- m1 v 0sin- m 1- m 2C- m2 v0cos-m1-m2D- m1-m2-m0-m1-m2

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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 $α$ with horizontal . Find the recoil speed of cannon if it is placed on ice.

\frac{m_{2} v_{0} cos α}{(m_{1} + m_{2})}

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\frac{m_{1} v_{0} sin α}{(m_{1} + m_{2})}

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\frac{m_{2} v_{0} cos α}{(m_{1} - m_{2})}

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\frac{m_{1} v_{0} sin α}{(m_{1} - m_{2})}

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Solution

The correct option is A $\frac{m_{2} v_{0} cos α}{(m_{1} + m_{2})}$
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 $= v_{0} cos α - v$
Applying momentum conservation in horizontal direction, we have
$0 = m_{2} (v_{0} cos α - v) - m_{1} v$
$\Rightarrow v = \frac{m_{2} v_{0} cos α}{(m_{1} + m_{2})}$

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A cannon of mass m1 fires a shell of mass m2 with speed v0 relative to the barrel which is inclined at an angle α with horizontal . Find the recoil speed of cannon if it is placed on ice.

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 $α$ with horizontal . Find the recoil speed of cannon if it is placed on ice.