Question

a gun of man 20kg fires a bullet of mass 50g with velocity of 200m/s.Caluclate the velocity of the recoil of the gun.
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Answer 1

Given :

• Mass of gun = 20kg
• Mass of bullet = 50g = 0.05 kg
• velocity of bullet = 200 m/s
• Initially system is in rest, so velocity of gun = velocity of bullet = 0

To find :

Recoil velocity of gun (v)

Formula used :

• Conservation of linear momentum
• Linear momentum = mass × velocity

Solution :

✪ Linear movement remain conserved.

✪ Initial momentum = ( mass of gun × initial velocity of gun ) + (mass of Bullet × initial velocity of bullet)

➠ Initial Linear momentum = (20 × 0) + (0.05×0)

➠ Initial Linear momentum = 0

✪ Final linear momentum = ( mass of gun × final velocity of gun ) + (mass of Bullet × final velocity of bullet)

➠ Final linear momentum = (20 × v) + (0.05×200)

➠ Final linear momentum = 20v + 10

✪ According to conservation of Linear momentum, Initial Linear momentum = Final linear momentum

➠ 0 = 20v + 10

➠ 20v = -10

➠ v = (-10) ÷ 20

➠ v = -0.5 m/s

✪ v is negative because it's Recoil velocity ( opposite to direction of bullet)

ANSWER :

Recoil velocity of gun = 0.5 m/s