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# 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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- alexLv 74 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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