Answer to Question #138084 in Quantum Mechanics for Viccy

Question #138084
A cannon of mass M starts sliding freely down a smooth inclined plane at an angle α to the horizontal. After the cannon covered the distance l, a shot was fired, the shell leaving the cannon in the horizontal direction with a momentum p. As a consequence, the cannon stopped. Assuming the mass of the shell to be negligible, as compared to that of the cannon, determine the duration of the shot.
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Expert's answer
2020-10-15T10:43:56-0400

Solution

According to question velocity of cannon is2glsinα\sqrt{2gl \sin\alpha} down to inclined plane. using linear impulse momentum theorem

Δpx=Fxdt\Delta p_x=F_xdt

    pcosαM2glsinα\implies p\cos \alpha-M\sqrt{2gl\sin\alpha}

=MgsinαΔt=Mg\sin \alpha\Delta t


Δt=pcosαM2glsinαMgsinα\Delta t=\frac{p\cos \alpha-M\sqrt{2gl\sin\alpha}}{Mg\sin \alpha}


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