A stone is dropped from roof of building takes 5 s to reach the ground. The sound of striking is heard after 5.4 second after the stone is dropped. The velocity of sound is

Options

A. `312.5 ms^(-1)`
B. `332.5 ms^(-1)`
C. `352 ms^(-1)`
D. `392 ms^(-1)`

Answer

To solve the problem step by step, we will break down the information given and apply the relevant physics concepts.

### Step 1: Understand the problem
A stone is dropped from the roof of a building and takes 5 seconds to reach the ground. The sound of the stone striking the ground is heard 5.4 seconds after the stone is dropped. We need to find the velocity of sound.

### Step 2: Calculate the time taken for sound to travel
The total time from when the stone is dropped to when the sound is heard is 5.4 seconds. Since the stone takes 5 seconds to hit the ground, the time taken for the sound to travel from the ground to the observer is:
\[ \text{Time for sound} = \text{Total time} - \text{Time for stone} = 5.4 \, \text{s} - 5 \, \text{s} = 0.4 \, \text{s} \]

### Step 3: Calculate the height of the building
Using the formula for the distance covered under free fall, where the initial velocity \( u = 0 \) and acceleration \( g = 10 \, \text{m/s}^2 \):
\[ h = ut + \frac{1}{2} g t^2 \]
Substituting the values:
\[ h = 0 \cdot 5 + \frac{1}{2} \cdot 10 \cdot (5)^2 \]
\[ h = 0 + \frac{1}{2} \cdot 10 \cdot 25 \]
\[ h = 125 \, \text{m} \]

### Step 4: Calculate the speed of sound
Now that we know the height of the building (which is the distance the sound travels), we can calculate the speed of sound using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Speed of sound} = \frac{125 \, \text{m}}{0.4 \, \text{s}} \]
\[ \text{Speed of sound} = 312.5 \, \text{m/s} \]

### Conclusion
The velocity of sound is \( 312.5 \, \text{m/s} \).

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