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(D) Let the engine be at point $A$ initially and at point $C$ after $5 \, s$. The distance $AB = 0.9 \, km = 900 \, m$.The sound travels from $A$ to t

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$30$

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(D) Let the engine be at point $A$ initially and at point $C$ after $5 \, s$. The distance $AB = 0.9 \, km = 900 \, m$.The sound travels from $A$ to the hill at $B$ and reflects back to the engine at $C$.The total time taken $t = 5 \, s$ is the time taken by sound to travel the distance $AB + BC$.$t = \frac{AB}{v_{sound}} + \frac{BC}{v_{sound}}$$5 = \frac{900}{330} + \frac{BC}{330}$$5 	imes 330 = 900 + BC$$1650 = 900 + BC$$BC = 1650 - 900 = 750 \, m$.The distance traveled by the engine in $5 \, s$ is $AC = AB - BC = 900 \, m - 750 \, m = 150 \, m$.Therefore,the speed of the engine $v_{engine} = \frac{AC}{t} = \frac{150 \, m}{5 \, s} = 30 \, m/s$.

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 $5 \, s$. If the speed of sound in air is $330 \, m/s$,then the speed of the engine is .... $m/s$.

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