A stone is dropped into a well of 80m deep. The sound of splash is heard 4.20 sec after the stone is dropped. Find the velocity of sound in air.

The answer is not 500 it is 400

To find the velocity of sound in air, we can use the equation:

distance = velocity × time

Given that the stone is dropped into a well of 80m deep and the sound of splash is heard 4.20 sec after the stone is dropped, we can consider two parts:

1. The time taken for the stone to reach the bottom of the well:
Using the equation of motion, we know that the distance covered by the stone when dropped freely is given by:
distance = (1/2) × acceleration × time^2
Since the stone is dropped freely, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
Therefore, the distance covered by the stone is 80m.
Plugging in the values, we get:
80m = (1/2) × 9.8 m/s^2 × time^2

2. The time taken for the sound to reach the observer from the bottom of the well:
Given that the sound of splash is heard 4.20 sec after the stone is dropped, the time taken by the sound to reach the observer is 4.20 sec.

Now, we can add the times for the stone and sound to get the total time:
time = time for the stone + time for the sound
time = time for the stone + 4.20 sec

From equation 1, we can rearrange it to find the time for the stone:
time for the stone = √(2 × distance / acceleration)

Plugging in the values, we get:
time for the stone = √(2 × 80m / 9.8 m/s^2)

Substituting this time into the total time equation, we get:
time = √(2 × 80m / 9.8 m/s^2) + 4.20 sec

Now, we can rearrange the equation to find the velocity of sound:
velocity = distance / time

Plugging in the values, we get:
velocity = 80m / (√(2 × 80m / 9.8 m/s^2) + 4.20 sec)

To find the velocity of sound in the air, we can use the formula:

velocity = distance / time

In this scenario, the distance the sound travels is the depth of the well, which is 80m. The time it takes for the sound to reach the top of the well is given as 4.20 seconds.

Now we plug the values into the formula to calculate the velocity:

velocity = 80m / 4.20s = 19.0476 m/s

Therefore, the velocity of sound in air is approximately 19.05 m/s.

time to fall is from

80 = 4.9t^2
t = 4.04 s

time for sound to return: 4.20-4.04 = 0.16 s

80m/0.16s = 500m/s