Answer
$d = \sqrt {2.25t^2+10000}$
Work Step by Step
First, draw a visualisation of the problem as seen below to better understand the question.
Then, we can use the formula $distance = speed \times time$ to find the horizontal distance travelled by the hot air balloon.
(We want speed to be in ft/s, so 15 miles per hour converts to around 1.5 feet per second)
Since time is represented by the variable $t$, the horizontal distance travelled by the balloon is;
$x=st$
$x=1.5t$
Now, we can use Pythagoras's theorem to find the distance, $d$, from the balloon to the intersection.
$d = \sqrt {(1.5t)^2+100^2}$
$d = \sqrt {2.25t^2+10000}$
