Answer:
6.03 seconds
Step-by-step explanation:
Given
[tex]y = -16t\² + 96t + 3[/tex]
To solve this, we simply set the height to 0.
i.e. [tex]y = 0[/tex]
So, we have:
[tex]-16t\² + 96t + 3 = 0[/tex]
Solve using quadratic formula.
[tex]t = \frac{-b+-\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = -16[/tex]
[tex]b = 96[/tex]
[tex]c = 3[/tex]
[tex]t = \frac{-96+-\sqrt{96^2 - 4 * -16 * 3}}{2 * -16}[/tex]
[tex]t = \frac{-96+-\sqrt{9216 +192}}{-32}[/tex]
[tex]t = \frac{-96+-\sqrt{9408}}{-32}[/tex]
[tex]t = \frac{-96+-96.9948452239}{-32}[/tex]
[tex]t = \frac{-96+96.9948452239}{-32}[/tex] or [tex]t = \frac{-96-96.9948452239}{-32}[/tex]
[tex]t = \frac{0.9948452239}{-32}[/tex] or [tex]t = \frac{-192.994845224}{-32}[/tex]
[tex]t = -0.031088913245535[/tex] or [tex]t = 6.0310889132455[/tex]
Since time can't be negative, we have:
[tex]t = 6.0310889132455[/tex]
[tex]t = 6.03\ seconds[/tex] (approximated)
