An airplane is flying at a speed of 370 mi/h at an altitude of one mile and passes directly over a radar.....?

Question

An airplane is flying at a speed of 370 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(t) =

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

s(d) =

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

s(t) =

Answer 1

OK,

a)  d(t) = 370t (miles/hr)

b)  This is a triangle 1 mile high and d(t) long so, using Pythagorean Theorem, s(d) = (d^2 + 1^2)^(1/2)

c)  To express s(t), substitute 370t for d(t) in the above equation:

     s(t)=((370t)^2 + 1^2)^(1/2)

Answer 2

You forgot to include the possibility of Islamic terrorists in this equation. I couldn't possibly answer this without all pertinent information. Sorry.

Answer 3

a)  The plane is traveling at a constant speed of 370 mi/h, so we simply use the basic D = r x t formula.  Distance is a function of speed times the time traveled:  d(t) = 370 t.  Here t is in hours.

b)  The distance between the plane and the radar would have to be measured using the pythagorean theorem.  d gives the horizontal distance (perhaps call this x), and the vertical distance is a fixed 1 mile.  The formula expressing this is s^2 = 1^2 + d^2.  As the plane travels, the horizontal distance will of course increase, so s can be expressed as a function of d:  s(d) = sqrt(1 + d^2).

c)  Using composition, we simply insert d(t) in place of d:

s(t) = sqrt(1 + (370t)^2).