Answer
The golf ball travels a horizontal distance of 1456 feet.
Work Step by Step
$v = 88~ft/s$
$\theta = 45^{\circ}$
$h = 0$
We can find an expression for $y$ in terms of $t$:
$y = (v~sin~\theta)(t)-2.66~t^2+h$
$y = (88~sin~45^{\circ})(t)-2.66~t^2$
$y = 44~\sqrt{2}~t-2.66~t^2$
We can find the time the golf ball is in flight:
$y = 44~\sqrt{2}~t-2.66~t^2$
$44~\sqrt{2}~t-2.66~t^2 = 0$
$(44\sqrt{2}-2.66~t)(t) = 0$
$t = 0$ or $(44\sqrt{2}-2.66~t) = 0$
$t = \frac{44\sqrt{2}}{2.66}$
$t = 23.4~seconds$
The golf ball is in flight for approximately 23.4 seconds.
We can find the horizontal distance:
$x = (v~cos~\theta)(t)$
$x = (88~cos~45^{\circ})(t)$
$x = 44~\sqrt{2}~t$
$x = (44~\sqrt{2})(23.4)$
$x = 1456~feet$
The golf ball travels a horizontal distance of 1456 feet.
