# Answer to Question #15949 in Mechanics | Relativity for riley groom

Question #15949

use the law of cosines and the law of sines to find the ground speed of an airplane with an airspeed of 120 km/hr @ 20 degrees E of N if the wind is blowing 40 km/hr @ 10 degrees S of E

Expert's answer

To find ground speed we, for the beginning will find projections for vector of ground speed.

It'll be

V(grx)=V(plx)+V(wx)

V(gry)=V(ply)+V(wy),

where V is for velocity,

gr - ground

pl - plane,

w - wind.

x,y - for coordinates, where x- from W to E and y - from S to N.

V(plx)=V(pl)*sin20.

V(wx)=V(w)*sin20.

The same for y, but with cosinuses.

So,

V(gr)=(V(grx)^2+V(gry)^2)^-0.5.

V(grx)=47.9

V(gry)=72 kmh

V(gr)=88 kmh

It'll be

V(grx)=V(plx)+V(wx)

V(gry)=V(ply)+V(wy),

where V is for velocity,

gr - ground

pl - plane,

w - wind.

x,y - for coordinates, where x- from W to E and y - from S to N.

V(plx)=V(pl)*sin20.

V(wx)=V(w)*sin20.

The same for y, but with cosinuses.

So,

V(gr)=(V(grx)^2+V(gry)^2)^-0.5.

V(grx)=47.9

V(gry)=72 kmh

V(gr)=88 kmh

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