A soldier loads a 10 kg cannonball into a 300 kg cannon that is initially at rest on the ground.

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A soldier loads a 10 kg cannonball into a 300 kg cannon that...

A soldier loads a 10 $\mathrm{kg}$ cannonball into a 300 $\mathrm{kg}$ cannon that is initially at rest on the ground. What is the recoil speed of the cannon if the cannonball is fired with a horizontal velocity of 300 $\mathrm{m} / \mathrm{s}$ ? (A) 5 $\mathrm{m} / \mathrm{s}$ (B) 7.5 $\mathrm{m} / \mathrm{s}$ (C) 10 $\mathrm{m} / \mathrm{s}$ (D) 15 $\mathrm{m} / \mathrm{s}$

A soldier loads a 10 $\mathrm{kg}$ cannonball into a 300 $\mathrm{kg}$ cannon that is initially at rest on the ground. What is the recoil speed of the cannon if the cannonball is fired with a horizontal velocity of 300 $\mathrm{m} / \mathrm{s}$ ?
(A) 5 $\mathrm{m} / \mathrm{s}$
(B) 7.5 $\mathrm{m} / \mathrm{s}$
(C) 10 $\mathrm{m} / \mathrm{s}$
(D) 15 $\mathrm{m} / \mathrm{s}$

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Key Concepts

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant. It is a fundamental concept in mechanics that applies during interactions such as collisions or separations, where the momentum before the event is equal to the momentum afterwards. This principle is essential for analyzing problems where objects interact, as it enables the calculation of unknown velocities or masses in the system.

Newton's Third Law

Newton's Third Law states that for every action there is an equal and opposite reaction. This concept explains that when one object exerts a force on another, the second object exerts a force of equal magnitude in the opposite direction. It is crucial for understanding recoil in scenarios where an object is propelled in one direction, causing another object to move in the opposite direction.

Closed System

A closed system is one in which no external forces are acting, or their net effect is zero. In such systems, properties like momentum are conserved. Recognizing that a scenario can be treated as a closed system allows one to apply conservation laws effectively to analyze the behavior of the system following an interaction.

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