A plane in still air.

Question

You are flying a plane from Toronto to Ottawa (N65E). The wind is coming from N20W at 60 km/h. What should your speed relative to the still air and heading be if you are to make the 500km trip in 1h 15min?

Answer 1

From N65E, the destination is 35° above positive x-axis. The speed required to go 500 km in 1.25 hour is 400 km/h. The wind coming FROM N20W presents a vector from the origin at an angle 70° BELOW the positive x-axis. Sketch this out with lengths proportional to 400 and 60 km/h. To get the plane's desired velocity, we SUBTRACT wind velocity components from destination components.

In x, v_x = (400 cos 25) - [60 cos(-70)] = 342.0 km/h.

In y, v_y = (400 sin 25) - [60 sin(-70)] = 225.4 km/h. Required air speed v = √(v_x² + v_y²) = 410 km/h.

Direction relative to x-axis is tan^-1 (225.4 / 342.0) = 33.4°, from which the bearing is N56.6E.