Drop a stone in a well, the sound is heard 17 seconds later. How deep is the well in feet
d = -16t^2 , if we have to consider direction
or
d = 16t^2 if all we care about is distance
when t = 17
d = 16(17)^2 = 4624 ft
some deep well !!
T1 = Time for stone to hit bottom.
T2 = Time for sound to reach top of well
T1 + T2 = 17 s.
T1 = 17-T2
0.5g*(17-T2)^2 = Vs*T2
4.9(289-34T2+T2^2) = 343T2
1416-167T2+4.9T2^2 = 343T2
4.9T2^2-510T2+1416 = 0
Use Quadratic formula and get:
T2 = 2.85 s.
T1 = 17-2.85 = 14.15 s.
d = Vs*T2 = 343 * 2.85 = 978 m = 3226 Ft
To find the depth of the well, we can use the formula:
Depth = (Speed of Sound * Time) / 2
The speed of sound in air is approximately 1,125 feet per second. Since the sound took 17 seconds to reach the top, we can plug in these values into the formula:
Depth = (1,125 ft/s * 17 s) / 2
Depth = 19,125 ft / 2
Depth = 9,562.5 ft
Therefore, the depth of the well is approximately 9,562.5 feet.
To determine the depth of the well, we can use the speed of sound as a reference. Sound travels at approximately 1,125 feet per second in dry air at room temperature.
Given the information provided, we know that the sound of the stone hitting the bottom of the well is heard 17 seconds after it is dropped.
So, to calculate the depth of the well, we need to multiply the time it takes for the sound to travel by the speed of sound:
Distance = Speed × Time
Distance = 1,125 ft/s × 17 s
Distance = 19,125 feet
Therefore, the depth of the well is approximately 19,125 feet.