Question

An airplane heads due north at $100m/s$ and a $30m/s$ cross wind blows from the east to the west. The resultant velocity of the airplane (relative to due north) is approximately

• A. $130m/s$
• B. $70m/s$
• C. $90m/s$
• D. $104m/s$

Answer 1

The correct option is D $104m/s$

The plane is heading north which is perpendicular to west (the direction the wind is pushing), therefore the resultant of these two vectors is the hypotenuse of a right triangle.
Using pythagorean theorem to find the magnitude of velocity vector,
$V^2=V_{plane}^2+V_{wind}^2{V}_{PG}^2=(100{)}^2+(30{)}^2{V}_{PG}\approx 104m/s$