Answer
The rocket is in flight for approximately 7.0 seconds.
The horizontal distance covered is 448 feet.
Work Step by Step
We can find the total time the rocket is in flight:
$y = 64~\sqrt{3}~t-16~t^2+8$
$64~\sqrt{3}~t-16~t^2+8 = 0$
$16~t^2-64~\sqrt{3}~t-8 = 0$
We can use the quadratic formula to find the time $t$ that the rocket is in flight:
$t = \frac{-(-64~\sqrt{3})\pm \sqrt{(-64~\sqrt{3})^2-4(16)(-8)}}{(2)(16)}$
$t = \frac{64~\sqrt{3}\pm 113.14}{32}$
$t = -0.72, 7.0$
Since time of flight must be positive, $t = 7.0~seconds$.
The rocket is in flight for approximately 7.0 seconds.
We can find the horizontal distance covered:
$x = 118.95~t$
$x = (64)(7.0)$
$x = 448~feet$
The horizontal distance covered is 448 feet.
