A military gun is mounted on a railroad car (m=1500 kg) as...

A military gun is mounted on a railroad car $(m=1500 \mathrm{kg})$ as shown in Figure P7.34. There is no frictional force on the car, the track is horizontal, and the car is initially at rest. The gun then fires a shell of mass $30 \mathrm{kg}$ with a velocity of $300 \mathrm{m} / \mathrm{s}$ at an angle of $40^{\circ}$ with respect to the horizontal. Find the recoil velocity of the car.

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Key Concepts

Conservation of Linear Momentum

This principle states that in an isolated system, where no external forces act, the total momentum remains constant before and after an event. In problems involving recoil or projectile motion, the horizontal component of the momentum is especially conserved because friction or other horizontal forces are assumed negligible.

Vector Component Decomposition

Analyzing the motion of objects often requires breaking vectors into their horizontal and vertical components. This is essential in determining the impact of forces or velocities in specific directions, such as separating the firing velocity of a projectile into parts that influence horizontal motion (which affects recoil) and those that do not.

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