Question

B) If the person wants to hear the
echo 0.5 s earlier, then how much
distance should he move, toward or
away from the cliff?
(a) 595 m away from the cliff
(b) 255 m towards the cliff
(c) 85 m towards the cliff
(d) 255 m away from the cliff.​

Answer 1

Answer:

(b)255 m towards the cliff

Answer 2

Given,

The person wants to hear the echo 0.5 s earlier

To find,

Distance by which the person has to move

Solution,

We can solve this numerical problem by using the following process.

Now,

Let us assume that the distance of the man from the cliff is dm, the time for the person to hear the echo is t s, and the speed of the sound is 330 m/s.

We know that,

⇒ Speed = $\frac{d}{t}$

⇒ 330t = 2d (Equation 1)

According to the question, the person wants to hear the echo 0.5s earlier.

Thus,

The man will move towards the cliff. The time taken by sound will be less. Let the distance traveled by the man towards the man be x m.

⇒ 330 = $\frac{2(d-x)}{t-0.5}$

⇒ 330 (t-0.5) = 2(d-x)

⇒ 330t - 165 = 2d - 2x

From equation 1,

⇒ 330t - 165 = 330t - 2x

⇒ -165 = -2x

⇒ x = 82.5m

As a result, the distance moved by the man is 82.5 m.