Aplane is capable of flying at a speed of 180 km/hr in still air. the pilot takes off from an airfield and heads due north to the plane's compass. after 30 minutes of flight time the pilot notices that the plane has actually traveled 80 km at an angle of 5 degrees east of north due to wind,

(a) what is the wind velocity?

(b) in what direction should the pilot have head to reach the intended destination?

a) Vw = ( 13.9 km/h ; -20.6 km/h )

b) 4.4º NW

Explanation:

a) Vw = wind velocity ; Vp = isolated plane velocity ; Vr = real plane velocity

Vr = Vp + Vw

║Vr║ = 80 km / 0.5 h = 160 km/h

Vr = ( 160 sin(5º) ; 160 cos(5º) ) km/h = ( 13.9 ; 159.4 ) km/h

Vp = ( 0 ; 180 ) km/h

Vw = Vr - Vp = ( 13.9 ; 159.4 ) km/h - ( 0 ; 180 ) km/h

Vw = ( 13.9 ; -20.6 ) km/h

b) Vw = wind velocity ; Vp = isolated plane velocity ; Vr = real velocity

Vp = ( 180 sin(θ) ; 180 cos(θ) ) km/h

Vrₓ = 0 ⇒ Vpₓ + Vwₓ = 0 ⇒ 180 sin(θ) + 13.9 = 0

θ = arc sin (-13.9/180) = -4.4º

4.4º NW

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