• August 28th 2010, 10:19 PM
florx
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!
• August 29th 2010, 12:24 AM
Educated
(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.
• August 29th 2010, 10:06 AM
florx
Thank you so much Educated for helping me with this problem!