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?

1 Answer
Nov 9, 2015

Answer:

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!

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