Question

A person standing between two vertical cliffs and 640 m away from the nearest cliff, shouted. He heard the first echo after 4 s and the second echo 3 s later. The distance between the cliffs is

• A. 1120 m
• B. 2240 m
• C. 1280 m
• D. 1760 m

Answer 1

The correct option is D 1760 m

Consider the nearest cliff is A.
To hear the first echo:

Distance travelled by the sound $=x+x=2x=2\times 640m=1280mTime=4s$

Speed of sound, $v=\frac{\text{Total distance travelled}}{\text{Total time take}}=\frac{1280}{4}=320m/s$

To hear the second echo 3s later:

Distance $=y+y=2y$

Time $=4s+3s=7s$

Speed of sound, $v=320m/sNowv=\frac{2y}{t}\Rightarrow y=\frac{vt}{2}=\frac{320\times 7}{2}\Rightarrow y=1120m$

Total distance between the cliffs $=x+y=640+1120=1760m$

Hence, the correct answer is option (d).