SOLUTION: The distance an object falls is directly proportional to the square of the time has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

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Question 118224: The distance an object falls is directly proportional to the square of the time has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?
in one second it falls 216 feet, I took 1296/6 which equals 216, but then I sort of got lost.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You could use proportions to answer this question:
d+=+kt%5E2 "The distance, d, an object falls is directly proportional the square of the time, t, it has been falling"
You are first given that it takes 6 seconds (t = 6) to fall 1296 feet (d = 1296). Substitute these values for t and d into the equation above to find the value of k, the proportionality constant.
1296+=+%286%5E2%29k
1296+=+36k Divide both sides by 36.
k+=+36
So now the equation is: d+=+36t%5E2
Now you can answer the given question of finding t when d = 2304 feet.
2304+=+36t%5E2 Divide both sides by 36.
64+=+t%5E2 Take the square root of both sides.
t+=+8seconds.