How do i solve this? An airplane heads N60°E at 600 mi/h in still air. A tail wind begins to blow in the direction N30°E at 50 mi/h. Find the resulting speed of the airplane and its resulting direction of travel. Draw a diagram

1 Answer
May 23, 2018

Let us first understand what does "N"60^@"E" mean.
It is: We go 60^@ towards east from reference north direction.

Now lets take east as +x-axis and north as +y-axis.
As such airplane's v_s speed in still air makes an angle of 30^@ with the +x-axis and tail wind v_w makes an angle of 60^@ with it.
Let R be resultant of both. Resolving all there along the xand y-axes and equating both we get, for components along x-axis

R_x=v_(sx)+v_(wx)
=>R_x=600\ cos 30^@+50\ cos 60^@
=>R_x=600sqrt3/2+50xx1/2
=>R_x=519.62\ mph

Similarly, for components along y-axis

R_y=v_(sy)+v_(wy)
=>R_y=600\ sin 30^@+50\ sin 60^@
=>R_y=600xx1/2+50xxsqrt3/2
=>R_y=343.30\ mph

Now R=sqrt(R_x^2+R_y^2)

=>R=sqrt((519.62)^2+(343.30)^2)
=>R=622.8\ mph

If theta is angle made by resultant with x-axis then

theta=tan^-1(R_y/R_x)
theta=tan^-1(343.30/519.62)
theta=33.5^@
This can also be written as "N"56.5^@"E"

Please make a diagram and post here.