A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 600 km/hour along a horizontal line at 7750 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60 degrees north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.

Hint:

Hint: Use kilometers! not meters.

The plane flies at a constant height above the ground, but it does not fly at a constant height above sea level.

Actual applications are harder to get correct than theoretical questions. :-)

Find a unit vector in the (3 dimensional) direction the plane is flying.

Find the vector r(t)