A 500-kg cannon and a supply of 74 cannon balls, each with a mass of 26.0 kg, ar

Question

A 500-kg cannon and a supply of 74 cannon balls, each with a mass of 26.0 kg, are inside a sealed railroad car with a mass of 36000 kg and a length of 50 m. The cannon fires to the right; the car recoils to the left. The cannon balls remain in the car after hitting the wall. After all the cannon balls have been fired, what is the greatest distance the car can have moved from its original position?

I tired solving it many times but yet wrong answer help please

A 500-kg cannon and a supply of 74 cannon balls, each with a mass of 26.0 kg, are inside a sealed railroad car with a mass of 36000 kg and a length of 50 m. The cannon fires to the right; the car recoils to the left. The cannon balls remain in the car after hitting the wall. After all the cannon balls have been fired, what is the greatest distance the car can have moved from its original position?

Explanation / Answer

Note that the total momentum of the system is 0.

Also, the canon and car has total mass 36500 kg, which is 1404 times more massive than a ball.

Thus, they travel 1404 times slower than the ball.

Hence, if d = 50 m is travelled by each ball, then the car travels

dcar = 50/1404 = 0.035616 m per ball.

Thus, as there are 74 balls,

dtotcar = 2.636 m [ANSWER]

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