Is relative velocity confusing in multiple vector systems?

[Hijaz Aslam]

Are the vectors resolved correctly? I get a different answer to this question(well my diagram itself is different). How can $\beta$ be greater than $\alpha$?

Isn't it that here $\alpha$ should be in place of $\beta$ and $\beta$ in place of $\alpha$ and both $V(rain,woman)$ and $V(rain)$ should be in each others place?

 

[NTW]

I believe that the diagram is wrong. The V(woman) vector should be transported to the right, starting at the tip of V(rain), and the sum should be constructed putting the end of V(woman) at the tip of V(rain). As the vectors of the picture seem to be to scale, the sum vector will lean to the right, clearly...

 

[nasu]

The speed of the rain in respect to ground vg is given by
v_g=v_rw+v_w

where v_rw is the speed of the rain in respect to the woman and v_w is the speed of the woman.
Take these as velocities (vectors) and this is what they have there.

If the woman runs against the rain, the horizontal component of the rain's velocity should be larger from the point of view of the woman than from the ground. The vertical component is not changed. So the angle is larger.

 

[NTW]

The speed of the rain in respect to ground vg is given by
v_g=v_rw+v_w

where v_rw is the speed of the rain in respect to the woman and v_w is the speed of the woman.
Take these as velocities (vectors) and this is what they have there.

If the woman runs against the rain, the horizontal component of the rain's velocity should be larger from the point of view of the woman than from the ground. The vertical component is not changed. So the angle is larger.

Yes, I was wrong in my post above... Imagining the rain falling vertically, running in any direction will result in the angle perceived by the runner growing more and more horizontal the faster he runs...

 

[Hijaz Aslam]

The speed of the rain in respect to ground vg is given by
v_g=v_rw+v_w

where v_rw is the speed of the rain in respect to the woman and v_w is the speed of the woman.
Take these as velocities (vectors) and this is what they have there.

If the woman runs against the rain, the horizontal component of the rain's velocity should be larger from the point of view of the woman than from the ground. The vertical component is not changed. So the angle is larger.

Oh yes. This relative velocity baffles me always :(

Nasu - thanks for your reply. Your answer cleared it. If you don't mind can you look into this problem in my thread ( https://www.physicsforums.com/threa...taining-multiple-vectors.777125/#post-4887266 ) Relative velocity catches me there too :( .