In studying the relationship between the distance an aircraft travels along the runway before takeoff and the time spent accelerating from rest, the following data were collected:

1. (TI-83) Use the quadratic regression feature on your calculator to find a function of the form D(t) = at²+bt+c that best fits the given data.
2. In fitting the data to a quadratic function, what are we assuming about the acceleration of the aircraft?
3. Suppose the aircraft becomes airborne when its speed reaches 200 km/h.
   1. How long does it take the aircraft to become airborne?
   2. How far does the aircraft travel down the runway in this time?
4. Suppose that a pilot intends to take off after traveling 900 m down the runway. What would be her takeoff speed in km/h?
5. While testing some new equipment, a military reconnaissance plane flies over the runway at an altitude of 7.5 mi at a steady rate of 370 mi/h. Using radar, the crew of the reconnaissance plane observes an aircraft that has just taken off from the runway. The crew determines that at the instant the line-of-sight distance from their plane to the aircraft below is 9 mi, that distance is decreasing at a rate of 412 mi/h. If the instruments on the reconnaissance plane are correct, what is the takeoff speed of the aircraft in km/h?