Question

An airplane has an airspeed of 500 kilometers per hour bearing N45°E. The wind velocity is 60 kilometers per hour in the direction N30°W. Find the resultant vector representing the path of the plane relative to the ground?

Answer 1

Use unit vectors to solve the addition of two vectors.

Explanation:

Airplane : `500[cos(45)i+sin(45)j]=500[sqrt2/2i+sqrt2/2j]`

Wind : `60[cos(120)i+sin(120)j]=60[-1/2i+sqrt3/2j]`

Next, sum the two vectors:

Sum `=323.5534i+405.5149j`

Angle of resultant vector: `Tan^-1(405.5149/323.5534)~~51.414^o`
or `~~N38.6^oE`

Magnitude of resultant vector: `sqrt(323.5534^2+405.5149^2)~~518.7766` km/hr

Here is a sketch of the plane vector `(AB)` and the wind vector `(AC)`. The resultant vector is `AD`

hope that helped!