You are traveling on an airplane The velocity of the plane w

You are traveling on an airplane. The velocity of the plane with respect to the air is 130 m/s due east. The velocity of the air with respect to the ground is 49 m/s at an angle of 30° west of due north.

1) What is the speed of the plane with respect to the ground?____ m/s

2) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east). ___° East of due North

3) How far east will the plane travel in 1 hour? ____ m

Solution

Given,

velocity of the plane w.r.t the air = 130 m/s

velocity of the plane w.r.t the ground = 49 m/s

theta = 30 degrees

1)

speed of the plane w.r.t the ground =  velocity of the plane w.r.t the air + velocity of the plane w.r.t the ground

a = 130 - 49*sin(theta) = 130 - 49*sin 30 = 105.5 m/s

b = 49*cos(theta) = 49*cos 30 = 42.434 m/s

magnitude = sqrt(105.5^2 + 42.424^2) = 113.71 m/s

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2)

theta = tan^-1(b/a) = tan^-1(42.434 / 105.5) = 21.91 degrees North of East

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3)

Distance = V*t = 105.5 m/s* 3600 s = 379800 m