what does this mean and how do i get the answer?

Question

A windsurfer sails from Kingston sailing club with the intention of landing due

south of the club, on Wolfe Island. The normal summer wind is blowing from the S42°W at

40 knots. If the windsurfer can maintain a velocity of 50 knots, what direction must

she sail to guarantee arriving at her planned destination?

Answer 1

Student Susan came across this post and asked for help.

A vector for the Wind is <40cos(228),40sin(228)>.

Let θ represent the direction that the surfer must head in order to have the wind take him directly south.

The vector for that direction will be: <50cosθ,50sinθ>.

The resultant for adding those two vectors:

<40cos228+50cosθ, 40sin228+50sinθ>

In order for the resultant direction to be due south the x-component of that vector must be 0.

40cos228 + 50 cosθ = 0

50cosθ = -40cos228

cosθ = -4/5 cos228

θ = cos^-1(-4/5 cos228) ≈ 57.6^•

Since the direction is due south place θ in the 4th quadrant.

θ₂ = 360 - θ ≈ 302.4^•

This translates to S 32.4^• E. If the windsurfer heads in that direction at 50 knots the wind will take him due south.

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