A stone is dropped into a well, and the sound of the splash is heard in 7.7 seconds, if the velocity of sound be 343 m/s, find depth of the well.
time=time to fall+timeforsoundtoReturn
7.7=1/2 g h^2 + h/343
solve for h.
343 into 7.7
To find the depth of the well, we need to calculate the time it took for the stone to reach the bottom of the well.
Since the sound of the splash is heard in 7.7 seconds, we can assume that it took the same amount of time for the stone to fall to the bottom and for the sound to reach the top of the well.
The time it takes for the stone to fall can be calculated using the equation:
t = sqrt((2 * d) / g)
Where:
t = time
d = depth of the well
g = acceleration due to gravity (approximately 9.8 m/s^2)
Rearranging the equation to solve for d:
d = (t^2 * g) / 2
Substituting the given values:
d = (7.7^2 * 9.8) / 2
= 298.78 meters
Therefore, the depth of the well is approximately 298.78 meters.
To find the depth of the well, we can use the formula:
Distance = Speed × Time
In this case, the distance is the depth of the well, the speed is the velocity of sound, and the time is the time it takes for the sound to travel back up the well.
Given that the velocity of sound is 343 m/s and the time it takes for the sound to travel back up the well is 7.7 seconds, we can substitute these values into the formula:
Depth of the well = 343 m/s × 7.7 seconds
Calculating this, we get:
Depth of the well = 2641.1 meters
Therefore, the depth of the well is 2641.1 meters.