Vivekanand Vellanki

Lets draw a figure first. The figure below shows the well - the water is at a depth of h from the upper edge of well's wall. A stone travels a distance of h; hits the water; and the sound wave of the splash travels to the top in 3.5 seconds.

Let the stone take t1 seconds to hit the water. That is h=16t_1^2. In the remaining 3.5-t_1seconds, the sound wave travels a distance of h.

Given the speed of sound, we get \left(3.5-t_1\right)\cdot1087=h=16t_1^2.

[We haven't been given the units for the distance covered by the stone in t seconds. Let's assume, the units are in feet]

Solving, this quadratic equation will fetch the value of t_1and hence the depth of the well (h).