[deleted]
Hi Eckard,
I figured that you wouldn't take what I said about him seriously. My main concern is that prejudicial classification of someone based on ethnicity is frowned upon here in Canada (and downright bordering on unlawful) -- and for good reason. Perhaps he was born in Montana, and your classification was totally prejudicial and wrong. So, do you know for sure that what you said about him was true, or are you simply being prejudicial? I won't hold my breath while waiting for a logical, reasonable answer.
Anyway, if the wind velocity is W = and the cyclist velocity is V = , then the velocity of the air relative to the cyclist is R = W - V = . Altogether, the cyclist feels a drag in the direction opposite of their movement and, yes (like you're saying), also in the same direction of the wind. The important thing is that you need to subtract the velocities in order to get the air's velocity relative to the cyclist.
Perhaps I can give you a few extra examples in order to illustrate my point of view.
Consider the case where there is no wind: W = ; V = ; R = . The cyclist feels a drag pointing in the direction opposite of their movement. The cyclist "creates" a wind that does not exist in the rest frame, which gives rise to drag.
Also consider the case where the wind and the cyclist have the same velocity: R = . The cyclist negates the wind that exists in the rest frame, and so there is no drag.
It is from this vector R which you will obtain the speed (vector length) to be squared.