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An automatic gun fires 360 bullets per minute with a speed of \(360 \mathrm{~km} / \mathrm{h}\). If each bullet weighs \(20 \mathrm{~g}\), the power of the gun is
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The correct answer is:
\(600 \mathrm{~W}\)
Speed of each bullet, \(v=360 \mathrm{~km} / \mathrm{h}\)
\(=360 \times \frac{5}{18} \mathrm{~m} / \mathrm{s}=100 \mathrm{~m} / \mathrm{s}\)
Number of bullets fired per minute, \(N=360\)
Kinetic energy of 360 bullets,
\(k^{\prime}=N \times\) kinetic energy of each bullet
\(\begin{aligned}
& =360 \times \frac{1}{2} m v^2=360 \times \frac{1}{2} \times 0.02 \times 100^2 \\
& =3.6 \times 10^4 \mathrm{~J}
\end{aligned}\)
\(\begin{aligned}
\therefore \text { Power of gun } & =\frac{\text { Total energy }}{\text { Time }} \\
& =\frac{3.6 \times 10^4}{60}=600 \mathrm{~W}
\end{aligned}\)
\([\because\) Time, 1 minute \(=60 \mathrm{~s}\)]
\(=360 \times \frac{5}{18} \mathrm{~m} / \mathrm{s}=100 \mathrm{~m} / \mathrm{s}\)
Number of bullets fired per minute, \(N=360\)
Kinetic energy of 360 bullets,
\(k^{\prime}=N \times\) kinetic energy of each bullet
\(\begin{aligned}
& =360 \times \frac{1}{2} m v^2=360 \times \frac{1}{2} \times 0.02 \times 100^2 \\
& =3.6 \times 10^4 \mathrm{~J}
\end{aligned}\)
\(\begin{aligned}
\therefore \text { Power of gun } & =\frac{\text { Total energy }}{\text { Time }} \\
& =\frac{3.6 \times 10^4}{60}=600 \mathrm{~W}
\end{aligned}\)
\([\because\) Time, 1 minute \(=60 \mathrm{~s}\)]
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