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maths/physics/biomechanics

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At the beginning of a race, a yacht crosses the start line and sails in
westerly direction at a speed of 4 m s-1. The current of the sea is flowing at
2 m s-1 towards the north-east. Calculate how far [8 marks] and in what
direction (relative to west) [8 marks] the yacht has traveled after 10
minutes from its crossing the start line.
The answer is
(-4,0) + (1.4,1.4) = (-2.6,1.4)
= 2.96 m/s at W28.3°N
After 10 minutes (600 seconds) the distance traveled is 1772m

Can you show me how to work this out. thanks!

  • maths/physics/biomechanics - ,

    4m/s @ 180 Deg + 2m/s @ 45 Deg.

    X = 4*cos180 + 2*cos45 = -2.586 m/s.
    Y = 0 + 2*sin45 = 1.414 m/s.

    tanAr=Y/X = 1.414 / -2.586 = -.054687,
    Ar = -28.7 Deg. = Reference angle.
    A=-28.7 + 180=151.3 Deg.,CCW= W28.7Deg
    N.

    V = X/cosA = -2.586 / cos151.3 = 2.95 m/s @ W28.7Deg.N.

    d = 2.95m/s * 600s = 1770 m.

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