Answer
$\theta=66^{\circ}$
Work Step by Step
We see that the ball needs to travel 15 feet horizontally and 1.8 feet up. We first convert everything into metric units:
$15\ ft = 4.572 m$
$1.8 \ ft = .54864m$
$26 \ ft/s = 7.9248 \ m/s$
We know the following equations:
$\Delta x = v_{x0}t$
$\Delta y = v_{y0}t - \frac{1}{2}gt^2$
We use the first equation to find:
$4.572=26cos\theta t$
$t =\frac{.1758}{cos\theta}$
We plug this into the second equation to obtain:
$\Delta y = 26sin\theta(\frac{.1758}{cos\theta})-\frac{1}{2}(9.81)(\frac{.1758}{cos\theta})^2$
$.54864 = 7.9248sin\theta(\frac{.1758}{cos\theta})-\frac{1}{2}(9.81)(\frac{.1758}{cos\theta})^2$
Solving this equation gives:
$\theta=66^{\circ}$
