Edits to “Statement”, “Answer”
en/2.2.13.md
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| ### Statement | |||
| − | $2.2.13.$ [Insert the problem statement] | ||
| − | |||
| − | ### Solution | ||
| − | |||
| − | ### Statement | ||
| − | |||
| $2.2.13.$ 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. | |||
| @@ -16,7 +10,3 @@Solution | |||
| #### Answer | |||
| $S/L = 35/36$ | |||
| − | |||
| − | #### Answer | ||
| − | |||
| − | [Insert a concise answer or boxed result] | ||
| @@ -1,11 +1,5 @@ | |||
| ### Statement | ### Statement | ||
| $2.2.13.$ [Insert the problem statement] | |||
| ### Solution | |||
| ### Statement | |||
| $2.2.13.$ 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? | $2.2.13.$ 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 | ### 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 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. | 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. | ||
| @@ -16,7 +10,3 @@Solution | |||
| #### Answer | #### Answer | ||
| $S/L = 35/36$ | $S/L = 35/36$ | ||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||