Final answer:
An object that falls 16 feet in 1 second will take 3 seconds to fall 144 feet; we use the direct variation formula d = kt^2 and solve for the time.
Step-by-step explanation:
The question is regarding the time it takes for an object to fall a certain distance when it is known that the distance varies directly with the square of the time. Since an object falls 16 feet in 1 second, and the distance varies directly with the square of time, we can use the formula d = kt^2, where d is distance, t is time, and k is the constant of variation.
We are given that 16 feet corresponds to 1 second, so k can be found with 16 = k(1)^2, thus k = 16. We want to find out how long it takes the object to fall 144 feet. Using the formula again: 144 = 16t^2. Solving for t, we get t^2 = 144/16 which simplifies to t^2 = 9. Taking the square root gives us t = 3 seconds. Therefore, it will take 3 seconds for the object to fall 144 feet.