Physics

The pilot of an aircraft wishes to fly due
west in a 50.0 km/h wind blowing toward
the south. The speed of the aircraft in the absence of a wind is 228 km/h.

a) How many degrees from west should the
aircraft head? Let clockwise be positive.
Answer in units of degrees.

b) What should the plane’s speed be relative to the ground? Answer in units of km/h

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  1. a. Vpa = Vpg + Va = -228 km/h
    Vpg - 50i = -228
    Vpg = -228 + 50i

    Tan Ar = Y/X = 50/-228 = -0.21930
    Ar = -12.4o = Reference angle.

    A = -12.4 + 180 = 167.63oC CCW = 12.4o N. of W. = Heading.

    b. Vpg = X/CosA = -228/Cos167.63 = 233.4
    km/h. = Plane's speed relative to gnd.

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