Answer: 6 seconds
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Step-by-step explanation:
x = time in seconds
y = height of the penny at time x
The free-fall equation we use is
y = -16x^2 + 576
We don't know what x is, but we do know that y = 0 represents when the penny hits the ground (at height 0).
Plug in y = 0 and solve for x.
y = -16x^2 + 576
0 = -16x^2 + 576
16x^2 = 576
x^2 = 576/16
x^2 = 36
x = sqrt(36)
x = 6
We only consider the positive version of the square root since negative time values for x make no sense.
The penny takes 6 seconds to hit the ground when it starts at a height of 576 feet.
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Keep in mind that this problem ignores air resistance, which will play a factor in slowing the penny down. The air pushes upward to get in the penny's way, in a similar way how a parachute works.
Meaning that the actual fall time is going to be a bit longer than 6 seconds. For the sake of simplicity, we ignore air resistance because it greatly complicates the problem.