Question

In the figure, there are two boys, A and B standing on the two peaks of hill of same height and s is the distance between peaks. A shouts and B hears two sounds at an interval of 0.5 s. If speed of sound in air is v, then height of peaks is

Answer 1

Answer will be . 1/4[v^2+4sv]^1/2

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Answer 2

The value of height is h = 1 / 4 √ v^2 + 4 VS

Explanation:

We are given:

• The interval of sounds = 0.5 s
• To find: the heights of peaks.

Solution:

• Let's suppose the height = x
• Disatance = S
• Velocity = V
• Time for original sound = Distance / Speed

Time= S / V

Time = S / V + 1 / 2

t = 2S + V / 2V

Distance of echo = V x 2s + v / 2 v = 2 s + v / 2

By using phythagorus theorem.

OA^2 - AL^2 = LS^2

√ (2S + V / 4)^2 - (S / 2)^2 =

h = 4S^2 + v^2 + 4 Vs - 4S^2 / 16

h = 1 / 4 √ v^2 + 4 VS

Thus the value of height is h = 1 / 4 √ v^2 + 4 VS