The distance an object falls is directly propotional to the square of the time it has been falling. Afterr 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?
I can't even imagine how to figure tis out. I would appreciate your help.
Thanks
Since the distance fallen is proportional to the square of the time, the time required is proportional to the square root of the distance.
The distance increases by a factor 2304/1296.
Calculate the square root of that factor. Multiply that new number by 6 seconds for the time that it has been falling.
Here is another way to do it that might look simpler.
X = c t^2
X is the distance fallen.
c is a constant. t is the time
Use X = 1296 and t = 6 to solve for c.
c = 1296/36
Using that vaue of c, then solve
2304 = c t^2 for the time.
t^2 = (2304/1296)*36
To find the time it will take to fall 2304 feet, we can use the proportionality relationship between distance fallen and the square of the time.
First, let's find the constant of proportionality, which we'll call "c". We can do this by using the given information that after 6 seconds, the object has fallen 1296 feet.
We have the equation: X = c * t^2
Substituting X = 1296 and t = 6, we get:
1296 = c * 6^2
1296 = 36c
c = 1296/36
c = 36
Now, we can use this value of c to solve for the time it will take to fall 2304 feet.
Let's set up the equation:
2304 = 36 * t^2
Dividing both sides by 36, we get:
t^2 = 2304/36
t^2 = 64
Now, take the square root of both sides to solve for t:
t = √64
t = 8
Therefore, it will take 8 seconds for the object to fall 2304 feet.