[SOLVED] An airplane heads due north at 650km/h. It experiences a 60km/h crosswind flowing in the direction N 30 degrees W.

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1) Express the velocity of the airplane relative to the air in component form.

2) Express the velocity of the wind in component form.

3) Find the true velocity of the airplane as a velocity of the airplane as a vector.

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Kruger

Lainther

1) The velocity of the airplane relative to the air (V_airplane) is the sum of the velocity due north (V_north) and the crosswind (V_crosswind).

V_north = (650 \cos 0^\circ, 650 \sin 0^\circ) = (650, 0)

V_crosswind = (60 \cos(30^\circ), -60 \sin(30^\circ)) \approx (51.96, -30)

Now, add these vectors:

V_airplane = V_north + V_crosswind = (650 + 51.96, 0 - 30) = (701.96, -30)

2) V_wind = V_crosswind = (51.96, -30)

3) The true velocity V_true is the sum of the velocity of the airplane relative to the air and the velocity of the wind:

V_true = V_airplane + V_wind = (701.96 + 51.96, -30) = (753.92, -30)

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