Airplane and radar station functions

**leftyguitarjoe** · September 1st 2008, 12:35 PM

An airplane is flying at a speed of 200 mi/h at an altitude of one mile and passes directly over a radar station at time t = 0.

(a) Express the horizontal distance d (in miles) that the plane has flown as a function of t.

d = 200t
ok, well that was easy

(b) Express the distance s between the plane and the radar station as a function of d.

ok, now I'm kinda unsure here, so I drew a couple of pictures.

Airplane and radar station functions-1.jpg

Airplane and radar station functions-2.jpg

(beautiful, I know)

When I look at this, I see triangles. One leg is constantly 1 while the other increases according to d = 200t, and the hypotenuse is what I'm going for.... or so I think.

$s = \sqrt{d^2 + 1^2}$
so far so good.

and now for part C
(c) Use composition to express s as a function of t.
so, its like $f(g(x))$ (but with different letters)?

I tried $s = \sqrt{200t^2 + 1^2}$ and it was deemed incorrect.