A cannon on a railroad car is facing in a direction parallel to the tracks as sh

Question

A cannon on a railroad car is facing in a direction parallel to the tracks as shown in the figure. The cannon can fire a 100-kg cannonball at a muzzle speed of 180 m/s at an angle of ? = 20? above the horizontal. The cannon plus railway car have a mass of 2,000 kg. If the cannon and one cannon ball are traveling to the right on the railway car a speed of v = 14 m/s, what is the speed of the railway car (in m/s) after the cannon fires the cannonball? Assume that the track is horizontal and there is no friction. The muzzle speed is the velocity of the cannonball relative to the muzzle of the cannon in the rest frame of the cannon.

The answer is 5.54

Explanation / Answer

Here ,

let the speed of railway car be v

as there is no external force in horizontal direction ,

Using conservation of momentum in horizontal direction

14 * (2000 + 100) = v*2000 + 100*(180*cos(20))

v = 6.94 m/s

the final speed of the railway is 6.94 m/s

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