An airplane is flying South with a speed of 400 mph when it encounters a crosswind blowing East at 100 mph. Find the resulting velocity of the airplane (speed and direction).

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Dcochran · Answer 1 · 2023-08-28T10:43:56+0000

Answer:

Vs = -400 j speed of plane in still air

Vw = 100 i speed of wind encountered

V = Vs + Vw vector speed of speed respect to ground

V = 100 i - 400 j vector speed of plane

V = (100^2 + 400^2)^1/2 = 412 mph measured speed of plane

tan θ = Vy / Vx = -400 m/ -100 = 4

θ = 76 deg Plane flies southwest (straight south is 90 deg)

Assuming an easterly wind is blowing from the east as specified by weather