Answer
a) $f(t)=d=350t$, where t is measured in hours and d is measured in miles.
b) $F(d)=s=\sqrt (d^{2}+1)$
c)$F(f(t))=\sqrt ((350t)^{2}+1)$
Work Step by Step
a) We know that when t=0, d, the horizontal distance travelled is also 0. Therefore, if the airplane is moving at 350mi/hr, we can find the distance travelled by multiplying the speed and the time travelled. Hence, $f(t)=d=350t$.
b) Think of a a right triangle on the x-y plane. On the x plane, we have the distance traveled of the airplane, d, or $f(t)=d=350t$. On the y plane, or the height of the triangle, we have 1 mile.
We solve for the hypotenuse of the triangle (which will be equal to s, the distance between the radar station and the plane).
$s^{2}=d^{2}+1^{2}$. To isolate s we can take the square root of both sides to obtain:
$F(d)=s=\sqrt (d^{2}+1)$.
c) To create this $F(f(t))$ function, all we need to do is to substitute our known equation for d into the $F(d)$ equation, yielding:
$F(f(t))=\sqrt ((350t)^{2}+1)$
