A GI Joe squad in their submarine is in pursuit of a Cobra submarine. The GI Joe

Question

A GI Joe squad in their submarine is in pursuit of a Cobra submarine. The GI Joe commander knows he must be within 100 meters of the Cobra sub to launch a torpedo that will cripple it. The commander sends a sonar ping at a frequency of 2000 Hz and receives a reflected signal 0.631 seconds later at a frequency of 2010 Hz. If the speed of the GI Joe sub is 10.0 m/s, how long must the commander wait, after receiving the reflected ping, to fire the torpedo? (Note: the speed of sound in water is 1420 m/s.)

Explanation / Answer

speed of sound in water = 1420 m/s

time of reception = 0.631 s

so distance travelled by sound in this time = 1420 * 0.631 = 896.02 m

this has both to and fro distances.

In this time the GI joe ship moves by 10* 0.631 = 6.31 m

so if distance between GI joe and cobra at sonar ping = x

x + x-6.31 = 896.02  

x = 451.165 m

so present distance = 451.165 - 6.31 = 444.855 m

so Gi joe should wait 444.855 / 10 = 44.49 seconds

Hence, the commander must wait for 44.5 s

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