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An engine approaches a hill with a constant speed. When it is at a distance of $0.9 \mathrm{~km}$, it blows a whistle whose echo is heard by the driver after $5$ seconds. If the speed of sound in air is $330 \mathrm{~m} / \mathrm{s}$, then the speed of the engine is :
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The correct answer is:
$30 \mathrm{~m} / \mathrm{s}$
$30 \mathrm{~m} / \mathrm{s}$
Let after $5 \mathrm{~sec}$ engine at point $\mathrm{C}$
$\begin{aligned}
& \mathrm{t}=\frac{\mathrm{AB}}{330}+\frac{\mathrm{BC}}{330} \\
& 5=\frac{0.9 \times 1000}{330}+\frac{\mathrm{BC}}{330} \\
& \therefore \mathrm{BC}=750 \mathrm{~m}
\end{aligned}$
Distance travelled by engine in $5 \mathrm{~sec}$
$=900 \mathrm{~m}-750 \mathrm{~m}=150 \mathrm{~m}$
Therefore velocity of engine
$=\frac{150 \mathrm{~m}}{5 \mathrm{~sec}}=30 \mathrm{~m} / \mathrm{s}$
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