Question

1. If the distance to the water level in a well is doubled, is the time it takes to hear the splash twice what it was before, more than twice, or less than twice? Explain your answer.

Answer 1

If the distance to the water level in a well is doubled, the time it takes to hear the splash is less than twice what it was before.

It is so because, let initially the well depth is 5 m ,

therefore using the equation of motion, we get:

h = (1/2)gt^2

5 = (9.8/2)t^2

t = 1.01 s

Now, in case 2 , let depth of well is doubled , that is d = 10 m

10 = (9.8/2)t^2

t = 1.43 seconds

so we can easily observe from the above two considered cases that the time taken is actually less than twice.

The reason behind is this , that the object dropped into the well is under a constant acceleration (g) , thus it keeps on covering more distances in equal intervals of time as it keeps on travelling for longer and longer duration of time.

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