Question

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.

Answer 1

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.