A railway flat car is rushing along a level frictionless track at a speed of 45m/s. Mounted on the car and aimed forward is a cannon that fires 65 kg cannon balls with a muzzle speed of 625m/s. The total mass of the car, the cannon, and the large supply of cannon balls on the car is 3500 kg. How many cannon balls must be fired to bring the car as close to rest as possible?

4 balls will be fired.

m1 = 3500, v1 = 45
m2 = 625, v2 = ?
apply "m1.v1=m2.v2"
answer comes about 3.8

is the speed of the cannon ball relative to the car or the ground??

To solve this problem, we need to consider the principles of conservation of momentum. The total momentum of the system before firing the cannon balls is equal to the total momentum after firing them.

Let's assume that "n" cannon balls are fired. The mass of each cannon ball is 65 kg, so the total mass of the fired cannon balls is 65n kg.

Before firing the cannon balls, the total momentum of the system is given by the formula:

Momentum_before = (mass_car + mass_cannon + mass_cannonballs) * velocity_car

Momentum_before = (3500 kg) * (45 m/s)

After firing the cannon balls, the car and the remaining cannon balls will have a velocity that is closer to 0 m/s. So the total momentum after firing the cannon balls is given by the formula:

Momentum_after = (mass_car_after + mass_remaining_cannonballs) * velocity_final

Since the car is brought to rest, the velocity_final is 0 m/s.

Now, according to the conservation of momentum principle:

Momentum_before = Momentum_after

(3500 kg) * (45 m/s) = (mass_car_after + mass_remaining_cannonballs) * 0

3500 * 45 = mass_car_after * 0 + mass_remaining_cannonballs * 0

157500 = mass_car_after

This means the mass of the car after firing the cannon balls is 157500 kg.

Now, we can calculate the mass of the remaining cannon balls:

mass_remaining_cannonballs = total_mass_of_fired_cannonballs - mass_car_after

mass_remaining_cannonballs = (65n kg) - (157500 kg)

Now, in order to bring the car as close to rest as possible, we need to maximize the remaining momentum, which means we need to minimize the mass_remaining_cannonballs.

To find the minimum mass of the remaining cannon balls, we need to find the minimum value of n that makes the mass_remaining_cannonballs positive:

65n - 157500 > 0

65n > 157500

n > 2415.38 (rounded)

Therefore, in order to bring the car as close to rest as possible, at least 2416 cannon balls must be fired.