Vectors Application Question ?

Pilot wishes to fly from Bayfield to Toronto, a distance of 195km on a bearing of 085 degrees. The speed of the plane in still air is 260km/h. A 20km/h wind is blowing on a bearing of 215 degrees. Remembering that she must fly on a bearing of 085 degrees relative to the ground (ie. the resultant must be on that bearing) find: 

a) the heading she should take to reach her destination

b)how long the trip will take  

1 Answer

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  • alex
    Lv 7
    4 weeks ago

    Draw diagram

    Resultant vector r on the bearing of 085 

    wind vector w , heading vector h

    trip time = t hours

    cosine rule in a triangle --->(20t)^2+195^2-2(20t)(195)cos(130) = (260t)^2

    ---> t = 0.79 hours

    angle

    sin(θ) = (20/260)sin(130) =0.0589 ---> θ = 3.4 degrees

    a/

    heading bearing 081.6 degrees 

    b/

    t = 0.79 hours

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