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.
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