a shell of mass 0.020 kg is fired by a gun of mass 100kg.if the muzzle speed of the shell is 80m/s.what is the recoil speed of the gun

conserve momentum:

.02*80 = 100v

To find the recoil speed of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing is equal to the total momentum after the firing.

The momentum of an object is calculated by multiplying its mass by its velocity.

Let's denote the mass of the shell as m1 (0.020 kg), the mass of the gun as m2 (100 kg), the muzzle speed of the shell as v1 (80 m/s), and the recoil speed of the gun as v2 (unknown).

Before firing:
The momentum of the shell is given by: p1 = m1 * v1
The momentum of the gun is given by: p2 = m2 * 0 (since it is initially at rest)

After firing:
The momentum of the shell is given by: p1' = m1 * 0 (since it comes to rest after being fired)
The momentum of the gun is given by: p2' = m2 * v2

According to the principle of conservation of momentum, the total momentum before firing (p1 + p2) should be equal to the total momentum after firing (p1' + p2').

Therefore, we can set up the following equation:
p1 + p2 = p1' + p2'

Substituting the values we have:
m1 * v1 + m2 * 0 = m1 * 0 + m2 * v2

Since we know that m2 is 100 kg and m1 is 0.020 kg, we can solve for v2:

0.020 kg * 80 m/s + 100 kg * 0 = 0.020 kg * 0 + 100 kg * v2

1.6 kg⋅m/s = 100 kg * v2

Dividing both sides by 100 kg:
1.6 kg⋅m/s / 100 kg = v2

Therefore, the recoil speed of the gun (v2) is approximately 0.016 m/s.