Aman drops a stone into a water well on his farm. he hears the sound of the splash 4.26s later. how deep is the well? the acceleration due to gravity is 9.8m/s^2 and the speed of sound in air is 313m/s. answer in units of m

First let us calculate the time required for the stone to drop, say t1.

We use the formula:

h = vi t1 + 0.5 g t1^2

where h is height, vi is initial velocity = 0

h = 4.9 t1^2

Then the time required for the sound to go up, say t2:

h = 313 t2 – 4.9 t2^2

The two heights are equal so equate:

4.9 t1^2 = 313 t2 – 4.9 t2^2

We know that:

t1 + t2 = 4.26

so,

t1 = t2 – 4.26

Therefore:

4.9 (t2 – 4.26)^2 + 4.9 t2^2 – 313 t2 = 0

4.9 (t2^2 – 8.52 t2 + 18.1476) + 4.9 t2^2 – 313 t2 = 0

4.9 t2^2 – 41.748 t2 + 88.92324 + 4.9 t2^2 – 313 t2 = 0

9.8 t2^2 – 354.748 t2 = -88.92324

t2^2 – 36.2 t2 = -9.0738

Completing the square:

(t2 – 18.1)^2 = -9.0738 + 327.61

t2 – 18.1 = ± 17.85

t2 = 0.25s, 35.95

t2 cannot be greater than 4.26 s, therefore correct one is:

t2 = 0.25 s

Therefore height of the well is:

h = 313 t2 – 4.9 t2^2

h = 313 * 0.25 – 4.9 * 0.25^2

h = 77.94 m = 78m

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

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