Free Fall Exercises

Exercise Four, Calculations For a Free Fall Distance Traveled During a Given Time.- A falling body travels 68 m in the last second of its free motion: Assuming that the body started from rest, determine how long it took to reach the ground and the altitude from which the body fells.

A convenient axis is one with origin at the point of dropping and pointing downward.

Let t₁ be the time one second before hitting the ground and h1 the corresponding distance traveled.

Let t₂ be the time to hit the ground and h₂ the corresponding distance traveled.

Then t₂ - t₁ = 1 s and h₂ - h₁ = 68 m.
h₁=½ ·(9.8m/s²)t₁²=4.9m/s²t₁ and h₂=½ ·(9.8m/s²)t₂²=4.9m/s²t₂.
4.9m/s²t₂²-4.9m/s²t₁²=68 m, and replacing t₁ by (t₂-1s) we get
4.9m/s²t₂²-4.9m/s²(t₂ -1s)²=68 m or 9.8t₂-4.9=68 , with t₂ in seconds giving t₂ = 7.4 s.

The altitude is then h₂ = 4.9m/s²(7.4 s)² = 268 m.

Other Free Fall Exercises:
Free Fall Exercises, Part One
Free Fall Exercises, Part Two

To See the Free Fall Physics Theory:
Go To Free Fall Theory

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