Answer

Verified

51.9k+ views

**Hint:**We need to calculate the time taken by the stone to reach the well at first and deduct that amount from the total time, which is \[3.12s\]. Depth of the well is given, therefore, this remaining time was taken by sound to reach the observer, and hence we can find the

**Complete step by step solution:**

In the question it is given that the splash is heard after \[3.12s\], this means that the stone reached the well and then the sound travelled back to the observer, this took \[3.12s\].

The following values are given to us:

Time after which the splash is heard \[ = 3.12s\]\[(t)\]

Depth of the well \[ = 45m\]

g \[ = 10m{s^{ - 2}}\]

Let \[{t_1}\] be the time taken by the stone to reach the water.

And \[h\] be the depth of the well \[ = 45m\]

We know, the three equations of motion, from there let us consider the equation which helps us to calculate the distance travelled from initial velocity, acceleration and time taken.

\[h = ut + \dfrac{1}{2}g{t_1}^2\]

Since the stone is thrown, we consider the initial velocity to be zero.

\[\therefore U = 0\]

So, \[h = \dfrac{1}{2}g{t_1}^2\]

Now, rearranging the equation, we get:

\[{t_1} = \sqrt {\dfrac{{2h}}{g}} \]

Putting the values, we obtain:

\[{t_1} = \sqrt {\dfrac{{2 \times 45}}{{10}}} s\]

On solving, we get:

\[{t_1} = 3s\]

Total time taken by the splash to reach the observer is \[ = 3.12s\], therefore, time taken for the sound to travel to the observer is: \[{t_2} = t - {t_1}\]

Therefore, \[{t_2} = (3.12 - 3)s = 0.12s\]

We know. Distance travelled by the sound is depth of the well, which is \[ = 45m\]

Thus, we can calculate the speed of sound, as we know:

$\Rightarrow$ \[Speed = \dfrac{{{\text{Distance travelled}}}}{{{\text{Time Taken}}}}\]

Putting the values, we obtain:

$\Rightarrow$ \[Speed = \dfrac{{45}}{{0.12}}\]

Thus, we finally arrive at:

$\Rightarrow$ \[Speed = 375m/s\]

This is the required solution.

**Therefore, option (B) is correct.**

**Note:**SI unit of speed is \[m/s\], so if we have distances given in kilometre and time given I hours, we must convert them to meters and seconds respectively, and not write \[km/hr\], as the unit of speed. Initial velocity of the stone is taken to be zero, as the velocity remains the same, with respect to the reference frame.

Recently Updated Pages

A small illuminated bulb is at the bottom of a tank class 12 physics JEE_Main

A metal wire is subjected to a constant potential difference class 12 physics JEE_main

Deflection in the galvanometer A Towards right B Left class 12 physics JEE_Main

Calculate the resistivity of the material of a wire class 12 physics JEE_Main

When an external voltage V is applied across a semiconductor class 12 physics JEE_Main

When a Voltmeter connected across the terminals of class 12 physics JEE_Main

Other Pages

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

According to classical free electron theory A There class 11 physics JEE_Main

In Bohrs model of the hydrogen atom the radius of the class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

In projectile motion the modulus of rate of change class 11 physics JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main