1992 Paper 1 Q10

Year: 1992
Paper: 1
Question Number: 10

Course: LFM Pure and Mechanics
Section: Newton's laws and connected particles

Difficulty: 1516.0 Banger: 1500.0

Newton's laws connected particles momentum conservation relative motion projectile cannon recoil work-energy theorem constant force

Problem

A projectile of mass \(m\) is fired horizontally from a toy cannon of mass \(M\) which slides freely on a horizontal floor. The length of the barrel is \(l\) and the force exerted on the projectile has the constant value \(P\) for so long as the projectile remains in the barrel. Initially the cannon is at rest. Show that the projectile emerges from the barrel at a speed relative to the ground of \[ \sqrt{\frac{2PMl}{m(M+m)}}. \]

No solution available for this problem.

Rating Information

Difficulty Rating: 1516.0

Difficulty Comparisons: 1

Banger Rating: 1500.0

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Problem source

A projectile of mass $m$ is fired horizontally from a toy cannon
of mass $M$ which slides freely on a horizontal floor. The length
of the barrel is $l$ and the force exerted on the projectile has
the constant value $P$ for so long as the projectile remains in the
barrel. Initially the cannon is at rest. Show that the projectile
emerges from the barrel at a speed relative to the ground of 
\[
\sqrt{\frac{2PMl}{m(M+m)}}.
\]

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