A dolphin moves in water towards an obstacle at a speed of 15 m/s. At 2m from the obstacle, it emits a signal whose speed in water is 1500 m/s.How much time does it take to receive the echo? If the...

A dolphin moves in water towards an obstacle at a speed of 15 m/s. At 2m from the obstacle, it emits a signal whose speed in water is 1500 m/s.

How much time does it take to receive the echo? If the response time of the dolphin is 0.1 s, can it avoid the obstacle?

Asked on by modioh

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kjcdb8er | Teacher | (Level 1) Associate Educator

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Let t be the time at which the dolphin receives the return signal, and let d be the distance that the dolphin travels in that time. Then,

d = t*15 m/s

The original distance D from the dolphin to the object is 2 m. When the dolphin recieves the signal, he is at position D - d from the object. So the total distance traveled by the ultrasonic signal is:

D + D - d = 2D - t*15 m/s = t * 1500 m/s

4 m = t*1485 m/s

t = 2.69 ms

At 2.69 ms, the dolphin has traveled d = 2.69 ms * 15 m/s  = 0.04 m. So the object is 1.96 m away from the dolphin. At 2.69 ms + 100 ms = 102.69 ms, the dolphin has traveled d = 102.69 ms * 15 m/s = 1.54 m. So, having responded with 0.46 m to spare, the dolphin easily misses the object.

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