what would be the planes resultant velocity ? (CHECK MORE INFO ON QUESTION)

Question

magine a plane goes to the north at 2.50x10 (to the power of 2), and the wind blows southeast at 75km per hour, what would be the planes resultant velocity ?

Answer 1

The plane's velocity is 250kph and the wind speed is 75kph. If the wind direction was directly from the south it would simply add to the plane's speed, but as it is from the southeast it loses about 30% of its speed compared to the plane because the vector is cos45=sqrt(2)/2=0.7071. (The angle between south and southeast is 45 degrees.) 75cos45=53 approx, the northerly component of the wind, so the combined speed is 250+53=303kph.