You are an air traffic controller at O'Hare airport in Chicago. The computers have just quit again and your radar screen display is not functioning. However, the radar is still sending back information as to the distance away, r (in miles), and the direction, (in radians, counterclockwise from East), for each airplane.

The following is what the radar shows for four airplanes. In each case, for 0 t 10 (minutes), sketch the path of the airplane, find its speed, and describe what the airplane is doing. You have to decide if there is any danger of collision.

 1. r = 3t + (t²/2) + 1,   = /2

 2. r = (t²/2) - 12t + 71,   =

 3. r = 25,   = (2)t

4.

[Hint: Find x(t) and y(t)].

 5. Is there any danger of collision among these four airplanes? Why?