To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. How high is the building if the splash is seen 5.6 seconds after the stone is dropped?


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Oddman answered
The height of a falling object can be approximated (assuming no air resistance) by
  h(t) = -16t^2 + h0
where h0 is the initial height of the object.
We are given h(5.6) = 0 and are asked to find h0.
  0 = -16*5.6^2 + h0
  16*5.6^2 = h0
  501.76 = h0
The height of the building is about 500 ft.
We are given time measured to 2 significant digits, so our answer can be no more accurate than 2 significant digits. If you want more significant digits than that, you must also use a more precise number for the standard gravity constant.
  (9.80665 m/s^2)/(2*.3048 m/ft) = 196133/12192 ft/s^2 ≈ 16.0870242782 ft/s^2
The metric value of standard gravity is a definition, so is exact.

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