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How to Calculate the Height for a Dropped Object With the Acceleration

For any object with low air resistance, the acceleration due to gravity near Earth's surface is the same -- 9.81 meters per second squared. If you know how long it takes an object to fall, you can use the acceleration to figure out its starting height by working backwards. Timing the fall of an object using an object then estimating its height with a stopwatch is one way to practice.

Instructions

- 1
  Write down the following equation: final height = initial height - 4.9 t^2, where t is the time in seconds it took for the object to reach the ground.
- 2
  Rearrange this equation to solve for initial height by adding 4.9 t^2 to both sides. This will give you the following:
  
  initial height = final height + 4.9 t^2
- 3
  Replace "final height" with 0, because the final height of the object is its height when it hits the ground. Your equation now reads as follows:
  
  initial height = 4.9 t^2
- 4
  Substitute the length of time it took the object to hit the ground for t, plug the numbers into your calculator and write down the answer.
  
  For example: If t = 10 seconds, 10^2 = 100, so initial height = 4.9 x 100 = 490 meters.

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