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 use the principle of direct variation to set up a proportion:

d1/t1^2 = d2/t2^2

Given that d1 = 784 feet, t1 = 7 seconds, and t2 = 3 seconds, we can plug in these values into the equation:

784/7^2 = d2/3^2

Simplifying the equation:

784/49 = d2/9

Cross multiplying:

d2 = (784/49) * 9
d2 = 144 feet

Therefore, if the object has been falling for 3 seconds, it has fallen 144 feet.