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?
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.