a coin is dropped into well and is heard to hit the water in 3.14 sec .. after being dropped determine the depth of the well
Answers
Answered by
1
The stone is dropped from top of the well. The level of water in the well is say 'h’ metre below the top of the well. When a stone is dropped from top of the well, it travels in air and then hits the top of water level in the well producing sound. It is this sound which takes 4 seconds to reach the top of the well from the moment the stone is dropped. Sound travels through air at 350 m/s.
Asking, what is depth of the well is a wrong question? Depth of the well means the distance between the bottom of the well and the top of the water level in the well.
The motion of stone, once it enters water will have forces of upthrust (due to water displaced ), and will fall with some terminal velocity and then hit the bottom of the well. The sound produced will first travel through water and then through air. Velocity of sound in water is much different then velocity of sound in air. The figure 350m/s is about the velocity of sound in air.
So what the post intends to know is how far below is water level from the top of the well, rather than what is the depth of the well.
I shall try to answer it in accordance with the above understanding of the post.
Let the level of water be 'h' metre below the top of the well, from where the stone is dropped.
Time taken by the stone to hit the water surface, can be found using the relation :
h = ½ g t². Taking g = 10m/s², we get
h = 5 t²,==> t = (h/5)½ —————————-(1)
The time taken by sound to travel h metre through air be t’ = (h/350)s.
Total time elapsed= ( h/5)½ + (h/350) = 4 s (given)——(2)
Equation 2 can be solved for h, by transposing h/350 to the RHS and then squaring the resulting equation. We get a quadratic equation,
h² —27,300 h + 1960000= 0
Solving yields h= 72 m, and 27,228m. The second figure is unrealistic and can be neglected.
The depth of water surface 72m below the top of the well is a reasonable figure.
IF U HAVE ANY DOUBTS COMMENT BELOW...
Asking, what is depth of the well is a wrong question? Depth of the well means the distance between the bottom of the well and the top of the water level in the well.
The motion of stone, once it enters water will have forces of upthrust (due to water displaced ), and will fall with some terminal velocity and then hit the bottom of the well. The sound produced will first travel through water and then through air. Velocity of sound in water is much different then velocity of sound in air. The figure 350m/s is about the velocity of sound in air.
So what the post intends to know is how far below is water level from the top of the well, rather than what is the depth of the well.
I shall try to answer it in accordance with the above understanding of the post.
Let the level of water be 'h' metre below the top of the well, from where the stone is dropped.
Time taken by the stone to hit the water surface, can be found using the relation :
h = ½ g t². Taking g = 10m/s², we get
h = 5 t²,==> t = (h/5)½ —————————-(1)
The time taken by sound to travel h metre through air be t’ = (h/350)s.
Total time elapsed= ( h/5)½ + (h/350) = 4 s (given)——(2)
Equation 2 can be solved for h, by transposing h/350 to the RHS and then squaring the resulting equation. We get a quadratic equation,
h² —27,300 h + 1960000= 0
Solving yields h= 72 m, and 27,228m. The second figure is unrealistic and can be neglected.
The depth of water surface 72m below the top of the well is a reasonable figure.
IF U HAVE ANY DOUBTS COMMENT BELOW...
Similar questions