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Question

Bullets of mass 10 g each are fired from a machine gun at a rate of 6 bullets/minute. The muzzle velocity of bullets is 100 m/s. The thrust force (in N) due to firing bullets experienced by the person holding the gun stationary is 10x. Find x.

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Solution

Given,
Mass of each bullet, m=10 g
m=101000=0.01 kg
Time taken by the gun to fire 6 bullets, T=1 min=60 s
Time taken by the gun to fire 1 bullet, t=T6
t=606
t=10 s
Initial velocity, u=0
Final velocity, v=100 m/s
Acceleration, a=vut
a=100010
a=10 m/s2
Force, F=m×a
F=0.001×10
F=0.1 N=101 N

According to Newton's third law, to every action, there is an opposite and equal reaction.
The thrust force due to firing bullets experienced by the person holding the gun stationery is 101 N
x=1

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