maths/physics/biomechanics
posted by alex on .
At the beginning of a race, a yacht crosses the start line and sails in
westerly direction at a speed of 4 m s1. The current of the sea is flowing at
2 m s1 towards the northeast. 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!

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.