An underwater but near the surface explosion is detected by

An underwater ( but near the surface) explosion is detected by sonar on a ship 20 s before it is heard on the deck. if sound travels at 6000ft/s in water and 1400 ft/s in air, how far is the ship from the explosion ? (round the answer to the nearest foot)

Solution

let time elapsed in detecting the explosion by sonar = t sec

explosion is detected by sonar on a ship 20 s before it is heard on the deck

time elapsed in hearing the explosion on deck = (t+20) sec

distance =velocity * time

distance sound travels in water = 6000*t

distance sound travels in air = 1400*(t+20)

both the distances are same

6000*t = 1400*(t+20)

6000t =1400t +28000

4600t =28000

t=(140_/23) sec

distance of  ship from the explosion =6000*t

distance of  ship from the explosion =6000*(140_/23)

distance of  ship from the explosion =36522 ft