Q. 4 - Calculus

Question

When flying home for the holidays, Eva often flies between Denver International Airport (DLA) and Chicago O'Hare (ORD). Suppose Eva's plane takes off from DIA and 50 miles from ORD the plane has to circle the airport because of snow. The plane circles ORD four times and then lands.

(a) Draw a graph depicting the distance from DIA to Eva's plane as a function of time.

(b) Draw a graph depicting the distance from ORD to Eva's plane as a function of time.

Step-by-Step Solution

Answer

a) graph depicting the distance from DIA to Eva's plane as a function of time is following.

(b) graph depicting the distance from ORD to Eva's plane as a function of time is following.

Step 1. Given information.

Eva’s plane takes off from DIA and the plane circles ORD four times from $50$miles before landing at ORD.

Step 2. Part (a)

Eva’s plane takes off from DIA so distance increases with time.

The distance from DIA to Eva’s plane is$D=f\left(t\right).$

Step 2. Part (b)

Eva's plane circles ORD four times from $50$miles before landing at ORD.

The distance from ORD to Eva’s plane is following.

 $$\begin{gathered} D=-f\left(t\right)+4\left(2\mathrm{\pi r}\right) \\ D=-f\left(t\right)+4(2\pi ·50) \\ D=-f\left(t\right)+400\mathrm{\pi } \end{gathered}$$