1.

A canon of mass M is mounted on an east west frictionless railway track. The barrel of cannon faces the north east direction at an angle of 45^(@) with the vertical. The canon fires a shot of mass M with a speed V relative to the barrel.

Answer»

The recoil speed of the cannon will be `V//4`
The speed of the SHOT as seen from the GROUND will be `(sqrt(13))/(4)V`.
The momentum of the shot `+`CANON system will remain conserved along the east west line.
The momentum of the shot plus canon system will remain conserved along the North South line.

Solution :Conserving momentum along the east west line
`M(v cos^(2)45-v_(0))=Mv_(0)`
`rArr 2MV_(0)=MV cos^(2)45^(@)`
`rArr v_(0)=V//4`
Vertical speed `=(v)/(sqrt(2))`
North speed `=v cos^(2)45^(@)=(v)/(2)`
East speed `=(V)/(2)-(V)/(4)=(V)/(4)`
`rArr` Speed from ground `=vsqrt((1)/(2)+(1)/(4)+(1)/(16))=vsqrt((13)/(16))`


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