question_answer

                An engine approaches a hill with a constant speed. When it is 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:                JEE Main Online Paper (Held On 09 April 2013)

A)                 32 m/s                

B)                 27.5 m/s                                              

C)                 60 m/s                 

D)                        30 m/s                

Correct Answer: D

Solution :

                                Distance travelled by engine \[=v\times 5\,m=x\]                 Distance travelled by sound \[=900+(900-x)\]                 \[=(1800-x)m\] \[\Rightarrow \]               \[{{v}_{sound}}=330\,m/s\] \[\Rightarrow \]               \[v=\frac{\text{distance}}{\text{t}}\]                 \[330=\frac{(1800-x)}{5}\]                 \[1650=1800-x\]                 \[x=1800-1650\]                 \[x=150\,m\]                 Speed of engine \[=\frac{x}{5}=\frac{150}{5}=30\,m/s\]