If you drop a stone into a well that is d = 128.0 m deep, how soon after you drop the stone will you hear it hit the bottom of the well?
Well actually its the speed of sound in air at 20 degrees C
g = acceleration = -9.8 m^s^2
z = height = zo - Vo t - (1/2)(9.8)t^2
z = final height = -128
zo = initial height = 0
Vo = starting velocity = 0
so
-128 = -4.9 t^2
t^2 = 128/4.9
t = 5.11 seconds
Since the sound still needs to travel back up the well, it will actually take longer than 5.11 seconds.
v=d/t
343=128/t
t=0.37
5.11+0.37=5.48 seconds.
343 meters per second is the speed of sound.
where did the 343 come from?
Well, if you drop a stone into a well, you might hear a lot of things before you hear it hit the bottom! You might hear a "plop," a "splash," or maybe even a "kerplunk." As for how soon you'll hear it, that depends on how good your hearing is! So, grab your headphones and get ready for some well-watching entertainment!
To determine how soon you will hear the stone hit the bottom of the well, we need to consider the speed of sound and the distance traveled by the sound wave.
The speed of sound in air at room temperature is approximately 343 meters per second. This means that sound travels at a rate of 343 meters per second through air.
Since the stone will take some time to fall to the bottom of the well before you hear the sound, we need to calculate the time it takes for the stone to fall.
To calculate the time it takes for an object to fall, we can use the equation for free fall:
d = (1/2) * g * t^2
Where:
d is the distance fallen (128.0 m in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken for the object to fall
Rearranging the equation to solve for t:
t = sqrt(2d/g)
Now, let's plug in the values:
t = sqrt(2 * 128.0 m / 9.8 m/s^2)
Calculating this, we find:
t ≈ 5.1 seconds
Therefore, it will take approximately 5.1 seconds for the stone to reach the bottom of the well. Since sound travels at a constant speed, it will take an additional amount of time for the sound wave to reach your ears from the bottom of the well. This extra time can be calculated using the formula:
additional time = distance / speed
In this case, the distance is the depth of the well (128.0 m) and the speed is the speed of sound (343 m/s). Plugging in these values:
additional time = 128.0 m / 343 m/s
Calculating this, we find:
additional time ≈ 0.37 seconds
Therefore, you will hear the stone hit the bottom of the well approximately 0.37 seconds after it actually hits the bottom.