The speed of an aircraft is sometimes expressed as a mach number: mach 1 means that the speed is equal to the speed of sound. if
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Define an x-y coordinate system such that
The positive x-axis = the eastern direction, with unit vector
.
The positive y-axis = the northern direction, with unit vector
.
The airplane flies at 340 km/h at 12° east of north. Its velocity vector is
The wind blows at 40 km/h in the direction 34° south of east. Its velocity vector is
![\vec{v}_{2} =40(cos(34^{o})\hat{i} - sin(24^{o})]\hat{j}) = 33.1615\hat{i} -22.3677\hat{j})](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D_%7B2%7D%20%3D40%28cos%2834%5E%7Bo%7D%29%5Chat%7Bi%7D%20-%20sin%2824%5E%7Bo%7D%29%5D%5Chat%7Bj%7D%29%20%3D%2033.1615%5Chat%7Bi%7D%20-22.3677%5Chat%7Bj%7D%29)
The plane's actual velocity is the vector sum of the two velocities. It is
The magnitude of the actual velocity is
v = √(121.1615² + 306.0473²) = 329.158 km/h
The angle that the velocity makes north of east is
tan⁻¹ (306.04733/121.1615) = 21.6°
Answer:
The actual velocity is 329.2 km/h at 21.6° north of east.
The positive x-axis = the eastern direction, with unit vector
The positive y-axis = the northern direction, with unit vector
The airplane flies at 340 km/h at 12° east of north. Its velocity vector is
The wind blows at 40 km/h in the direction 34° south of east. Its velocity vector is
The plane's actual velocity is the vector sum of the two velocities. It is
The magnitude of the actual velocity is
v = √(121.1615² + 306.0473²) = 329.158 km/h
The angle that the velocity makes north of east is
tan⁻¹ (306.04733/121.1615) = 21.6°
Answer:
The actual velocity is 329.2 km/h at 21.6° north of east.