Particles A and B move with speeds v₁ and v₂ along the positive x and negative y directions respectively, with initial separation d along y as shown. The least distance between them is:

Question

G1 Physics · Accepted Answer

Take A initially at origin and B at (0,-d). Relative position of B from A is r=(-v₁t)î+(-d-v₂t)ĵ depending on directions shown. Minimizing |r|² gives the perpendicular distance to the relative-motion line. From the source geometry this evaluates to d v₁/√(v₁²+v₂²). Option C.