SOLUTION: The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 50 ft in 5 seconds, how fa

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Question 1032106: The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 50 ft in 5 seconds, how far will it have fallen by the end of 9 seconds? (Leave the variation constant in fraction form or round to at least 2 decimal places. Round your final answer to the nearest foot.)
Found 3 solutions by josmiceli, ikleyn, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+50+=+k%2A5%5E2+
+50+=+k%2A25%0D%0A%7B%7B%7B+k+=+2+ ft/sec2
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+d+=+k%2At%5E2+
+d+=+2%2At%5E2+
+d+=+2%2A9%5E2+
+d+=+2%2A81+
+d+=+162+ ft
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Hope I got it

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground).
If an object fell 50 ft in 5 seconds, how far will it have fallen by the end of 9 seconds? (Leave the variation constant in
fraction form or round to at least 2 decimal places. Round your final answer to the nearest foot.)
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I will not consider the solution of this problem, but I'd like to make a small notice.

Near the Earth surface, the free fall acceleration is 32 ft%2Fs%5E2 (approximately. See this article of Wikipedia).

Accordingly, the free falling body falls %2832%2A5%5E2%29%2F2 = 400 ft in the first 5 seconds.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 50 ft in 5 seconds, how far will it have fallen by the end of 9 seconds? (Leave the variation constant in fraction form or round to at least 2 decimal places. Round your final answer to the nearest foot.)
With D being distance, k: constant of proportionality, and T, time (in seconds), we get: 
D+=+kT%5E2
50+=+k%285%29%5E2
matrix%281%2C5%2C+50%2F5%5E2+=+k%2C+or%2C+50%2F25+=+k%2C+or%2C+k+=+2%29
D+=+kT%5E2
D+=+2%289%29%5E2
D = 2(81), or highlight_green%28matrix%281%2C2%2C+162%2C+feet%29%29