9 A jet if flying through a wind that is blowing with a spee

9.) A jet if flying through a wind that is blowing with a speed of 60mph in the direction N50°E.The jet has a speed of 741mi/h in still air, and the pilot heads the jet in the direction N30°E. Find the true speed of the jet. Please show ALL you work.

Solution

Jet travels in direction with 741,N30E = < 740sin30 ,740cos30>

= < 370 , 640.85>

Velocity of wind with 60, N50E = < 60sin50 , 60cos50 >

=< 45.96 ,38.56>

Adding the above two vectors:

= < 415.96 , 679.41 >

True Velocity = sqrt(415.96^2 + 679.41^2) = 796.63 mi/h

Angle = tan^-1(679.41/415.96) = 58.52 = N58.52E (dierction)