In here we found first $$d(h) = \sqrt{h^2 + 0.25}$$ (the distance $d$ in terms of the distance $h$), and $$h(t) = 275t$$ (the distance $h$ in terms of the time $t$).

In  $d(h) = \sqrt{h^2 + 0.25}$, we cannot plug in $t$, since the input for this function is a distance $h$ in miles, and $t$ is time given in hours. 

When we found $d \circ h$, $$d\circ h(t) = \sqrt{(275t)^2 +0.25}$$ we were able to then give the distance $d$ in terms of the time $t$, so we can think of this composition as $d(t)$.

So, if the input is the horizontal distance from the control tower to the plane, we have $d = \sqrt{h^2 + 0.25}$, and if the input is the time that passed after the plane went through the control tower, we have $d = \sqrt{(275t)^2 + 0.25}$.