Velocity Direction

Earth View

Let the Nimitz be point A, and the F-15 be point B.

The origin of the x-y coordinate system is fixed relative to the earth.

The velocity of the Nimitz relative to the earth is

     v_A = 15j knots

The velocity of the F-15 relative to the Nimitz is

     v_B/A = 300 cos45i + 300 sin45j knots

Using the relative velocity equation, the velocity of the F-15 relative to the earth can be obtained as,

     v_B = v_A + v_B/A
          = 300 cos45i + (15 + 300 sin45)j
          = 212.1i + 227.1j

The magnitude of the velocity of the F-15 relative to the earth is

Trigonometry can be used to find the direction of the
F-15 relative to the earth, giving

     θ = tan^-1 (212.1/227.1) = 43.0^o East of North