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 f

Algebra ->  Radicals -> 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 f      Log On


   

Question 7249: 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(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = the distance the object has fallen.
Let t = the time it takes for the object to fall distance, d.
Then, you can write:
d+=+kt%5E2 Now you need 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.
%281296%2F36%29+=+k
36+=+k
Now you need to find the time, t, the object takes to fall 2304 ft. Solve the distance formula for t.
t+=+sqrt%28d%2Fk%29 Substitute d = 2304 and k = 36 and solve for t.
t+=+sqrt%282304%2F36%29
t+=+%2848%2F6%29
t+=+8+secs.