A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 625 km/hour at a constant height of 7500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60∘ 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.

Plane move from x to y axes. The parametric equations are:

X = f (t) , y = g (t)

The z coordinate of plane remain unchanged, so z = 0

Step-by-step explanation:

The position of a point particle r relative to fixed origin describes the location of the particle.

Evolution of r in time, we can use the law of motion for particle:

r = r (t)

This vector equation equal to the three scalar equations along the Cartesian axes.

X = x (t)

Y = y (t)

Z = z (t)

Distance of plane = 625 km/hour

Height = 7500 meters

Bismarck is about 850 km from Denver.

The distance of Bismarck = 850 – 625

                                    = 225 km / hour

Time can be calculated by the formula:

Time = distance / speed

The plane move Denver to Bismarck, let Denver is at x-axes and Bismarck at y-axes.

Plane move from x to y axes. The parametric equations are:

X = f (t) , y = g (t)

The z coordinate of plane remain unchanged, so z = 0