# A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s^-1, what is the recoil speed of the gun?

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A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s-1, what is the recoil speed of the gun?

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Given: m1 = 0.02 kg, m2 = 100 kg, v1 = 80 m s-1

To find: Recoil speed (v2)

Formula: m1u1 + m2u2 = m1v1 + m2v2

Calculation: Initially gun and shell are at rest.

∴ m1u+ m2u2 = 0

Final momentum = m1v1 – m2v2

Using formula,

0 = 0.02 (80) – 100(v2)

∴ v2$\frac{0.02\times80}{100}$ = 0.016 ms-1

The recoil speed of the gun is 0.016 m s-1.