Answer: Approximately 0.78388 seconds
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Explanation:
Plug in t = 0 to find that
h = -16t^2 - 64t + 60
h = -16(0)^2 - 64(0) + 60
h = 60
The starting height is 60 feet.
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Now plug in h = 0 and solve for t.
h = -16t^2 - 64t + 60
0 = -16t^2 - 64t + 60
-16t^2 - 64t + 60 = 0
From here use the quadratic formula
[tex]t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \frac{-(-64)\pm\sqrt{(-64)^2-4(-16)(60)}}{2(-16)}\\\\t = \frac{64\pm\sqrt{7936}}{-32}\\\\t = \frac{64+\sqrt{7936}}{-32} \ \text{ or } \ t = \frac{64-\sqrt{7936}}{-32}\\\\t \approx -4.78388 \ \text{ or } \ t \approx 0.78388 \\\\[/tex]
We ignore the negative t value as a negative time doesn't make sense.
The only practical answer is roughly t = 0.78388 seconds.
