Question

The distance a body falls from rest varies directly as the square of the time the body is falling. If a body falls 81 ft. in 3 seconds, how far will it fall in 7 seconds?

A) 162 ft
B) 441 ft
C) 324 ft
D) 60 ft

Answer 1

Using the direct variation formula for free-fall distance, we determine that a body falling for 7 seconds will cover 441 feet, which corresponds to option B) 441 ft.

Step-by-step explanation:

The distance a body falls from rest varies directly as the square of the time the body is falling. To solve the problem, we use the direct variation formula, which is d = k · t^2, where d is the distance, t is the time, and k is the constant of proportionality. Given that a body falls 81 ft in 3 seconds, we can find k by rearranging the formula to k = d / t^2.

We get k = 81 ft / 3^2, which simplifies to k = 81 ft / 9, and hence k = 9 ft/s^2. Now that we have k, we can find out how far the body will fall in 7 seconds by plugging t = 7 into the formula, yielding d = 9 ft/s^2 · 7^2, which simplifies to d = 9 ft/s^2 · 49, and so d = 441 ft. Therefore, the body will fall 441 feet in 7 seconds.