Question

Lindsay is planning a flight from St. Catharines to Hamilton, which lies due west of St. Catharines. Her aircraft flies at a speed of 200 km/h in still air.A wind of 50.0 km/h is blowing from [W 608 N]. In what direction must sheaim the airplane to fly directly to Hamilton?

Answer 1

Answer:

Lindsay is planning a flight from St. Catherines to Hamilton, which lies due west of St. Catharines. Her aircraft flies at a speed of 200 km/h in still air. A wind of 50.0 km/h is blowing from [W 60.0� N]. In what direction must she aim the airplane to fly directly to Hamilton?

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It's a triangle problem.

The long side is the 200 km/hr, at an angle to be determined.

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1 side is 50 km/hr at an angle of -60 degs or 300 degs.

The 3rd side's length is not known, but it's at an angle of 180 degs (along the x-axis).

Answer 2

Lindsay has to fly this plane towards this direction [W 12.5° S] to get to Hamilton.

From this question, the plane is still up in the air.

We have wind blowing in [W 60° N ]

To solve the problem we have to make use of the sine rule

$\frac{SinA}{a}=\frac{SinB}{b} =\frac{SinC}{c}$

We put the values in the equation, we have:

50/Sinθ = 200/sin60°

The next step is to cross multiply

50 x sin60° = 200Sinθ

50 x 0.8660 = 200sinθ

We make Sin θ the subject

Sine θ = 43.30/200

sine θ = 0.2165

we find the value of θ

θ = sine⁻¹(0.2165)

θ = 12.50

So Lindsay has to fly this plane towards this direction

[W 12.5° S]

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