Question

A person holding a rifle (mass of person and rifle together is $100kg$) stands on a smooth surface and fires $10$ shots horizontally, in $5s$. Each bullet has a mass of $10g$ with a muzzle velocity of $800m{s}^{-1}$. The final velocity acquired by the person and the average force exerted on the person are :

• A. -0.8 ms^-1 ; 16 N
• B. -0.8 ms^-1 ; 8 N
• C. -1.6 ms^-1 ; 16 N
• D. -1.6 ms^-1 ; 8 N

Answer 1

Answer: (A)

$<br/>P(\text{ initial })=P(\text{ final })<br/>$
$<br/>0=n\times m\times u+(M-n\times m)\times v<br/>$
where: $n=10,m=10g=0.01kg,u=800m/s,M=100kg$
$<br/>0=10\times 0.01kg\times 800m/s+(100kg-10\times 0.01kg)\times v<br/>$
$<br/>v=-\frac{80kgm/s}{99.9kgm/s}<br/>$
$<br/>v=-0.8m/s<br/>$
Then $:F=\frac{\Delta P}{\Delta t}=\frac{10\times 0.01kg\times 800m/s}{5s}=16N$