Question

An airplane leaves Skyharbor airport at 8:30 PM. His average flight speed is 585 mph. He travels at 43 degrees east of north. The first half of his flight he encounters a cross wind of 72 mph at a direction of 70 degrees west of north. The second half of the flight he encounters a tailwind of 53 mph which hits the plane at 55 degrees west of south. He lands at his destination in 4 hours and 56 minutes. What is his final position vector from Skyharbor airport?

Write the vector in component form

What is his final distance from skyharbor

What is his final direction or bearing from skyharbor

Answer 1

Let's do the various legs in component form:
585@N43°E = <399,428>
72@N70°W = <-68,25>
53@S55°W = <-43,-30>
To get the various distances, involved, multiply these speeds by the time spent flying. Then you can convert the final displacement back to polar form.

Answer 2

does it not matter if the 585 is the average speed?

Answer 3

only if you're interested in speed at various places along the way. But you are ultimately only interested in the distance traveled, which is avg speed * time