SOLUTION: the distance, D in feet traveled by a freely falling object is given by the equation D = 16t^2 where t is time in seconds. Use this formula to find the time it wold take for an ob

Question 628396: the distance, D in feet traveled by a freely falling object is given by the equation D = 16t^2 where t is time in seconds. Use this formula to find the time it wold take for an object to fall to the ground from a cliff that is 576 feet high
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
You've been given an equation that relates d (distance) and t (time) to each other. And you've been given a specific distance, 576, and been asked to find the time for that distance.

All we have to do is replace the "d" in the equation with 576 and then use algebra to solve for t:

Because of the squared term, this is a quadratic equation. You have learned several ways to solve these: Factoring, Quadratic Formula, completing the square and even directly finding the square root of both sides. (Normally this last option is not an option. Finding a square root of each side only works when there is a squared term but not a first power term. We have a "t-squared" term but no "t-term" so we can do this.).

Finding the square root directly, when it can be used, is usually the easiest way to solve a quadratic equation. This is how we will proceed:

We are fortunate that that not only can we use this method but also that both sides are perfect squares! (If you do not see that 576 is a perfect square, start factoring out perfect squares, 576 = 4*144 = 2^2*12^2, and you will see that it is made up entirely of perfect square factors.

In general, the hardest part of finding square roots is remembering the negative square roots. But in this problem the variable is time. We are not interested in negative values for time (that would be before we even dropped the object!) so can freely ignore the negative square root:
24 = 4t
Dividing both sides by 4:
6 = t
So the object will take 6 seconds to fall 576 feet.
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