If a person drops a pebble in a well of $100 m$ depth, after how much time (in seconds) will he be able to hear the sound?
Given:
Acceleration due to gravity, $g = 10 m s^{- 2}$
Speed of sound in air, $v = 343 m s^{- 1}$

$\sqrt{20} + 0.3 s$

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$\sqrt{20} s$

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$0.3 s$

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$20 s$

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Solution

The correct option is A
$\sqrt{20} + 0.3 s$

The question can be divided into two parts, where in the first part, the time taken by the pebble to reach the bottom is calculated and in the second part, the time taken by the sound wave to reach the top is calculated.
Given:
Initial velocity, $u = 0 m s^{- 1}$
Depth of the well, $s = 100 m$
Acceleration, $a = 10 m s^{- 2}$
Speed of sound, $v = 343 m s^{- 1}$

Let $t_{1}$ be the time taken by the pebble to hit the bottom.
From second equation of motion,
$s = u t_{1} + \frac{1}{2} a t_{1}^{2}$
$100 = (0 \times t_{1}) + (\frac{1}{2} \times (10) \times t_{1}^{2})$
$100 = 5 t_{1}^{2}$
$\Rightarrow t_{1} = \sqrt{20} s$

We know, $t i m e = \frac{d i s t a n c e}{s p e e d}$
Let $t_{2}$ be the time taken for the sound wave to reach from the bottom to the top of the well.
$t_{2} = \frac{s}{v} = \frac{100}{343} \approx 0.3 s$

Total time,
$t = t_{1} + t_{2}$
$= \sqrt{20} + 0.3 s$ .

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If a person drops a pebble in a well of $100 m$ depth, after how much time (in seconds) will he be able to hear the sound?
Given:
Acceleration due to gravity, $g = 10 m s^{- 2}$
Speed of sound in air, $v = 343 m s^{- 1}$

If a person drops a pebble in a well of $100 m$ depth, after how much time will he be able to hear the sound, starting from the time he drops the pebble? (Take $g = 10 m / s^{2}$ and speed of sound $= 343 m / s$ )

Tinku dropped a stone into a very deep well. He hears the sound 6.53 s after he dropped the stone. Find the depth of the well. Take acceleration due to gravity, g =10 $m s^{- 2}$ and $v_{s o u n d}$ = 340 $m s^{- 1}$ .

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If a person drops a pebble in a well of 100 m depth, after how much time (in seconds) will he be able to hear the sound? Given: Acceleration due to gravity, g=10 ms−2 Speed of sound in air, v=343 ms−1

If a person drops a pebble in a well of $100 m$ depth, after how much time (in seconds) will he be able to hear the sound?
Given:
Acceleration due to gravity, $g = 10 m s^{- 2}$
Speed of sound in air, $v = 343 m s^{- 1}$