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

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Question 128639: The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
First write the equation of variation:
d+=+kt%5E2 k is the constant of variation, d is the distance, and t is the time the object has been falling.
To find the value of k, substitute the given values of t = 6 secs. and d = 1296 ft.
1296+=+k%286%29%5E2
1296+=+36k Divide both sides by 36.
k+=+36 Now write the equation as:
d+=+36t%5E2 Substitute the given values of d = 2304 ft.
2304+=+36t%5E2 Divide both sides by 36.
t%5E2+=+64 Take the square root of both sides.
t+=+8 Use only the positive value.
It will take 8 seconds for the object to fall 2304 feet.