Question

A soldier with a machine gun, falling from an airplane gets detached from his parachute. He is able to resist the downward acceleration if he shoots 40 bullets a second at the speed of 500 m/s. If the weight of a bullet is 49 gm, what is the weight of the man with the gun ? Ignore resistance due to air and assume the acceleration due to gravity $g=9.8m/s^2$

• A. 50 kg
• B. 75 kg
• C. 100 kg
• D. 125 kg

Answer 1

The correct option is C 100 kg

Given : $m=0.049$ kg $v=500$ m/s $n=40$ bullets per sec

Let the mass of the man with the gun be $M$.

Force experienced by the man due to momentum of the bullets must be equal to gravitational force i.e $F=Mg$

Total change of momentum of the bullets per second $\frac{dP}{dt}=mnv$

$\therefore$ $F=\frac{dP}{dt}$ $⟹Mg=mnv$

OR $M\left(9.8\right)=\left(0.049\right)\left(40\right)\left(500\right)$ $⟹M=100$ kg