A bat, flying due east at 2 m/s, emits a shriek that is reflected back to it from an oncoming insect flying directly toward the bat at 4 m/s. The insect is 20 m from the bat at the instant the shriek is emitted. Sound travels 340 m/s in air. After what elapsed time does the bat hear the reflected echo?

0.1169 s

Explanation:

From the question, it is given that the bat emits the sound when it was at distance of 20.0 m from the insect

This then means that the time taken by the sound to reach the wall is given as

t1 = 20/340

t1 = 0.0588 s

Also, d1 = vt, so that

d1 = 2 * 0.0588

d1 = 0.1176 m, and this is the distance moved by the bat.

Next,

d' = 20 - 0.1176

d' = 19.8824 m is the distance between the bat and the wall.

t2 = d'/[v(c) + v]

t2 = 19.8824 / (340 + 2)

t2 = 19.8824 / 342

t2 = 0.0581 s

Total time, T = t1 + t2

T = 0.0588 + 0.0581

T = 0.1169 s

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