A machine gun fires 50gm bullets at a speed of 1000m/s. the Gunner, holding the machine gun in his hand, can exert an average force of 180N against the gun. determine the maximum number of bullets he can fire per minute.

We are given:

m = 50g OR  0.05 kg

v = 1000 m/s

Force applied by the gunner in a second = 180 N

Momentum(p) of the bullet:

p = mv

p = 0.05 * 1000

p = 50 kg m/s

Finding the recoil force:

The units kg m/s are also known as 'N' (newtons)

So, we can say that the force exerted on every bullet is 50 N

According to the law of conservation of momentum, every bullet fired applies a force of 50N towards the gunner

Hence, we can say that the recoil force of every bullet is 50N

Finding the number of bullets fired in a minute:

We are given that the gunner applied an average force of 180N on the gun

we know that that can also be written as 180 kg m/s. Notice the 's' in the units of the momentum, it tells us that this force is applied every second

So, to find the amount of force applied in a minute, we can multiply it by 60

Force applied by the gunner in a minute = (60 * 180) = 10800 N

Let n be the number of bullets fired in a minute

We can say that the force applied by the gunner is equal to the force applied by a bullet times the number of bullets fired

F(gunner) = n * F(bullet)

10800 = n * 50

n = 10800/50

n = 216 bullets / minute

The gunner shoots 216 bullets in a minute

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