Question

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.

Answer 1

Solution

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

$\Delta p_x=F_xdt$

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

$=Mg\sin \alpha\Delta t$

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