An engine approaches a hill with a constant speed. When it is at a distance of $0.9\, km$, it blows a whistle whose echo is heard by the driver after $5\, seconds$. If the speed of sound in air is $330\, m/s$, then the speed of the engine is .... $m/s$
JEE MAIN 2013, Diffcult
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Let after 5 sec engine at point $C$
$t=\frac{A B}{330}+\frac{B C}{330}$
$5=\frac{0.9 \times 1000}{330}+\frac{\mathrm{BC}}{330}$
$\therefore \mathrm{BC}=750 \mathrm{m}$
Distance travelled by engine in $5\, sec$
$=900 \mathrm{m}-750 \mathrm{m}=150 \mathrm{m}$
Therefore velocity of engine
$=\frac{150 \mathrm{m}}{5 \mathrm{sec}}=30 \mathrm{m} / \mathrm{s}$
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