Answer:
a) Vaw = 2.19 mi / h θ = 346.8º b) Vmgx = 0.866 mi / h Vawy = -0.5 mi / h
Explanation:
We using the sum of vectors, we use the indexes ‘a’ for the plane, ‘g’ for the land ‘w’ for the wind,
[tex]v_{ag}[/tex] = [tex]v_{aw}[/tex] + [tex]v_{wg}[/tex]
[tex]v_{aw}[/tex] = [tex]v_{ag}[/tex] + [tex]v_{wg}[/tex]
To facilitate the calculation we decompose with respect to xy coordinate system
[tex]v_{wgx}[/tex] = [tex]v_{wg}[/tex] cos 30
[tex]v_{wgy}[/tex]= [tex]v_{wg}[/tex] sin30
Vwgx = Vwd cos 30
Vwgx = Vwd sin30
Vmgx = 1.00 cos 30
Vmgx = 0.866 mi / h
Vmgy = 1.00 sin30
Vwgy = 0.5 mi / h
Let's find the resulting components
Vawx = 3.00 -0.866
Vawx = 2,134 mi / h
Vawy = 0 - 0.5
Vawy = -0.5 mi / h
Let's use Pythagoras' theorem
Vaw2 = Vawx2 + Vawy2
Vaw = Ra Vawx2 + Vawy2
Vaw = ra 2,134 2 + 0.52
Vaw = 2.19 mi / h
