Thanks for the correction. Yes, it seems I omitted (so conveniently) that asin is multivalued, so there can be up to two solutions.

However, using the law of cosines (instead of sines) fixes this inconvenience and also eliminates the need to use trigonometric functions.
Also, it'll be the solution with the relative velocity that has the larger magnitude (trivial).
Let's say <Va,Vba>/|Va|/|Vba|=cos(a)
So: Vba = sqrt(Va^2(cos(a)^2-1) + Vb^2) - Va*cos(a)

So still, no need to find the actual time of collision.

Thanks for the correction. Yes, it seems I omitted (so conveniently) that asin is multivalued, so there can be two solutions.

However, using the law of cosines (instead of sines) fixes this inconvenience and also eliminates the need to use trigonometric functions.
Also, it'll be the solution with the relative velocity that has the larger magnitude (trivial).
Let's say <Va,Vba>/|Va|/|Vba|=cos(a)
So: Vba = sqrt(Va^2(cos(a)^2-1) + Vb^2) - Va*cos(a)

So still, no need to find the actual time of collision.

Thanks for the correction. Yes, it seems I omitted (so conveniently) that asin is multivalued, so there can be two solutions.

However, using the law of cosines (instead of sines) fixes this inconvenience and also eliminates the need to use trigonometric functions.
Also, it'll be the solution with the relative velocity that has the larger magnitude (trivial).
Let's say <Va,Vba>/|Va|/|Vba|=cos(a)
So: Vba = sqrt(Va^2(cos(a)^2-1) + Vb^2) - Va*cos(a)