An airplane is flying at a speed of 100 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 = 100t (I came up with this answer and it is correct)

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

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

Please help me with the problems b and c. I don't understand what they are talking about. Like for d shouldn't the answer be 100d but the computer said it was incorrect. Please show your steps and explain how to solve these two problems (b) and (c). Thank you so much!

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

Since the plane has an altitude from the radar station of 1 mile, then you must use the pythagorus theorum:

$s^2 = d^2 + 1^2$

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

The answer would be 100d if the plane was on the same altitude as the radar station, but in this case it isn't.

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

Now you know that d = 100t, so you substitute that into equation (b) to express s as a function of t.

3. Thank you so much Educated for helping me with this problem!