2 Attachment(s)

Airplane and radar station functions

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.

Attachment 7668

Attachment 7669

(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.

$\displaystyle s = \sqrt{d^2 + 1^2}$

so far so good.

and now for part C

(c) Use composition to express *s* as a function of *t*.

so, its like $\displaystyle f(g(x))$(but with different letters)?

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