Question

Identical cannonballs are fired with the same force, one each from four cannons having respective bore lengths of 1.0 meter, 2.0 meters, 2.5 meters and 3.0 meters. Which cannon will have the minimum impulse on the ball if the force acting on the ball increases with the length of the bore?

Answer 1

most people are familiar with newton's second law looking like \[F = m*a\] but acceleration is just a change in velocity over time\[F = m *\frac {\Delta v}{\Delta t}\] Impulse is the property of force * time\[F* \Delta t = m * \Delta v\] If force increases with the length of the bore, then impulse will also increase with the length of the bore. If you're looking for the minimum impulse, the shortest bore will have the minimum impulse.