Quandaries and Queries


A cyclist is travelling in the direction of 12i+5j at a speed of 39 km/h where  i is a unit vector due east and j is a unit vector due north. The wind appears to the cyclist to be blowing with a velocity of (-4i+j) km/h. Find, correct to 1 d.p
(a) the true speed of the wind and
(b) the bearing from which the wind is blowing



What the cyclist perceives as the wind is a result of the true velocity of the wind and the cyclist's own velocity. Suppose that the velocity of the wind is

ai + bj

then what the cyclist perceives, -4i + j is the sum of 12i + 5j and ai + bj, that is

-4i + j = (12i + 5j) + (ai + bj)



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