The distance, d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 7 seconds has fallen 784 feet. Determine the distance the object has fallen if it has been falling for 3 seconds.
We can set up a proportion to solve this problem.
Let's set up the proportion using the information given:
(d1 / t1^2) = (d2 / t2^2)
Where d1 is the distance the object has fallen for 7 seconds, t1 is the time in seconds it has been in free fall for 7 seconds, d2 is the distance we want to find for 3 seconds, and t2 is the time in seconds it has been in free fall for 3 seconds.
Substitute the given values into the proportion:
(784 / 7^2) = (d2 / 3^2)
Simplify the equation:
(784 / 49) = (d2 / 9)
Cross multiply:
784 * 9 = 49 * d2
7056 = 49 * d2
Divide both sides by 49:
d2 = 7056 / 49
d2 ≈ 144
Therefore, the distance the object has fallen if it has been falling for 3 seconds is approximately 144 feet.