The velocity of the wind relative to the cyclist is determined as -15.3 km i - 3.5 km j.
The speed of the wind in x - direction and y - direction is calculated as follows;
v(w/c) = - 5 km(cos 45)i - 5km(sin45)j
v(w/c) = [- 3.5 i - 3.5 j ] km
velocity of wind with respect to cyclist = (-12 km i - 3.5 km i) - 3.5 km j
velocity of wind with respect to cyclist = -15.3 km i - 3.5 km j
Thus, the velocity of the wind relative to the cyclist is determined as -15.3 km i - 3.5 km j.
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