A plane is headed from Memphis, Tennessee, to Albuquerque, New Mexico, 1000 mi due west. The plane

Question:

A plane is headed from Memphis, Tennessee, to Albuquerque, New Mexico, 1000 mi due west. The plane flies at 250 mi/h, and the pilot encounters a 20 mi/h wind blowing from the northwest. (That means the direction of the wind makes a 45° angle below the x-axis.)
a. Write an equation modeling the southward component of the wind.
b. Write an equation modeling the eastward component of the wind.
c. If the pilot does not compensate for the wind, explain why the final equations for the flight are x = -250t + 20t cos 45° and y = -20t sin 45°.
d. What graphing window and range of t-values can you use to simulate this flight?
e. Solve the equation -1000 = -250t + 20t cos 45°. What is the real-world meaning of your answer?
f. Use your answer from 9e to find how far south of Albuquerque the plane ended up.