Answer
The balloon's speed will be 15.8 ft/s
The balloon's path will make an angle of $71.6^{\circ}$ with the horizontal.
Work Step by Step
The hot-air balloon's resultant vector is $(5.00~ft/s, 15.0~ft/s)$
We can find the magnitude of the vector which is the balloon's speed:
$v = \sqrt{(5.00~ft/s)^2+(15.0~ft/s)^2}$
$v = 15.8~ft/s$
The balloon's speed will be 15.8 ft/s
We can find the angle above the horizontal:
$tan~\theta = \frac{15.0}{5.00}$
$\theta = arctan(\frac{15.0}{5.00})$
$\theta = 71.6^{\circ}$
The balloon's path will make an angle of $71.6^{\circ}$ with the horizontal.
