Question

A cannon and a supply of cannonballs are in a sealed system railroad car. The car has a length of 20 meters, and a mass of 2000kg. The cannon fires to the right, the car recoils to the left. Fired cannonballs remain in the car after hitting the wall and land on the floor at the end of the car. The cannonballs have a mass of 15 kg each, and there are ten of them. (neglect mass of cannon) How far will the car move after all ten have been fired

Answer 1

The distance the car moves after all ten cannonballs have been fired is 1.5 meters

Step-by-step explanation:

The parameters given in the question are;

The length of the car = 20 meters

The mass of the of the cannon ball, m₁ = 2,000 kg

The direction the cannon fires = The right

The direction the car recoils = The left

The mass of each cannonball, m₂ = 15 kg

The number of cannonballs = 10

Let v₁ represent the speed of the car and let v₂ represent the speed of the cannonball, where momentum is conserved, we have;

m₁·v₁ = m₂·v₂

2000 × v₁ = 15 × v₂

400·v₁ = 3·v₂

Therefore, when the cannon ball travels 400 meters, the railroad car travels 3 meters

Similarly, when the cannon ball travels 400/20 = 20 meters, the distance the railroad car travels, d = 3/20 meters

We not that the railroad car and the car are brought to a stop each time the cannonball hits the watt

Therefore, the total distance moved by the car after all ten have been fired,
`d_(total)`, is given as follows;

`d_(total)` = d × The number of balls fired

∴
`d_(total)` = 3/20 meters per ball × 10 balls = 3/2 meters = 1.5 meters

The total distance moved by the car,
`d_(total)` = How far the car moves after all ten have been fired = 1.5 meters.