A jet heads N 60 degree E at a speed of 600 mih relative to

A jet heads N 60 degree E at a speed of 600 mi/h relative to the air. A wind begins to blow in the direction N 30 degree W at 50 mi/h. (see the figure) Express the velocity of the wind as a vector in component form. Express the velocity of the jet relative to the air as a vector in component form. Express the true velocity of the jet as a vector. Find the ground speed and true direction of the jet.

Solution

v^2 = 600^2 + 50^2 - 2(600)(50)cos120
v^2 = 362500 + 30000 = 392500
v = 626.5 mi/hr

626.5/sin120 = 600/sinx
sinx = 0.8294
x = 56.0 degrees

56.0 - 30 = 26.0 degrees