$2.2.13.$ An artilleryman fires a cannonball of mass $m$ from a cannon so that it falls into the enemy camp. Baron Munchausen, whose mass is $5m$, sits on the cannonball flying out of the cannon. What fraction of the way to the enemy camp will he have to walk?
Solution
The cannon transfers a specific impulse to the projectile such that a projectile of mass $m$ reaches the enemy camp. From kinematics, it is known that the range of a body thrown at an angle to the horizontal is proportional to the square of its initial velocity ($S \propto v^2$).
The mass of the projectile together with Munchausen is $6m$. Since the same impulse is transferred, the initial velocity will be six times less ($v' = v/6$). The distance covered by such a projectile will be $1/36$ of the original distance to the camp. This means that the remaining $35/36$ of the way will have to be walked.