# If a stone is dropped into a lake from a tower, thesound of splash is heard by a man after 11.5 s, thenwhat is the height of tower?

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mvcdc | Certified Educator

This problem involves a free-falling body, the rock. We know that it is dropped and so the initial velocity, `v_o` is `0`. The force of gravity is also acting upon the free-falling object, giving it a constant acceleration, the acceleration due to gravity, `g = 9.8 m/s^2.`

Assuming that there is no air resistance, we have the following formula for distance travelled, or the height from which the stone fell:

`h = v_o t + 1/2 g t^2`

Substituting what we know, we have:

`h = (0 * 11.5s) + 1/2 (9.8m/s^2)*(11.5s)^2`

`h = 0 + 1/2 (9.8 m/s^2) * (132.25s^2)`

`h = 648.025 m`

Hence, the tower has a height of 648.025 meters.

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