To solve this problem, you must figure out (in vector form)
both the wind vector and plane vector
w⃗ = wind vector
P⃗ = plane vector
To get the true course of the plane, you need to add the
plane and wind vectors, the formula would be
w⃗ +P⃗ ,
which will result to the
ground speed.
ground speed=||w⃗ +P⃗ ||
Using the planar representation of your situation, this will
help you understand the equation, use this to make the equation more
understandable.
w⃗ =AB¯¯¯¯¯¯¯¯, P⃗ =AC¯¯¯¯¯¯¯¯
the smaller circle is of radius 50 (similar to the wind
speed) and the larger circle is of radius 200 (similar to the plane vector. To get the coordinates of these two vectors, use polar coordinates.
Let East be 0 degrees, so since the wind vector is on the
circle of radius 50, we have:
w⃗ =⟨50cos(135),50sin(135)⟩=⟨−252√,
252√⟩.
P⃗ =⟨200cos(60),200sin(60)⟩=⟨100,\1003√⟩.
w⃗ +P⃗ =⟨100−252√ , 1003√+252√⟩
||w⃗ +P⃗ ||=(100−252√)2+(1003√+252√)2
√≈218.349218.
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