Splung.com Physics Forum

[amlyn]

An airplane is heading due south at a speed of 600 km/h. If a wind begins blowing from the southwest at a speed of 100 km/h (average), calculate: (a) the velocity (magnitude and direction) of the plane relative to the ground, and (b) how far from its intended position will it be after 10 min if the pilot takes no corrective action. [Hint: first draw a diagram] When I draw the diagram for this equation, I do not think that I have enough information to solve the problem, mostly because the relationship does not form a right triangle. I need to know how to draw the diagram and how to find the requested information.

[hepcj]

When you form an addition of vectors the resultant does not have to form a right-angled triangle. You can use the law of cosines which takes the length of two sides and the angle between them to find the size of the resulting vector.

c^2 = a^2 + b^2 - 2 a b cos(theta)

where a and b are the lengths of the sides, theta is the angle between and c is the resulting length.
You can find any the remaining angles using the law of sines when you know an angle and three sides.