Question

you are on an airplane traveling 30° south of due west at 120 m/s with respect to the air. the air is moving with a speed 47 m/s with respect to the ground due north. 1)what is the speed of the plane with respect to the ground?

Answer 1

Vp = 120 cos 210 + 120 sin 210 = Vi1 + Vy1 due East zero coordinates

Vp = -103.9 i - 60 j vector description of velocity of plane

Vw = 47 j vector description of wind

V = Vp + Vw = -103.9 i - 13 j

V = (103.9^2 + 13^2)^1/2 = 104.7

Cos θ = -103.9 / 104.7 = 187.1 deg X-component of final velocity

Sin θ = -13 / 104.7 = 187.13 deg Y-component of final velocity

(Final velocity = 104.7 m/s 7.1 deg S of W)