Two girls are standing at the ends 'A' and 'B' of a ground where A B=b . The girl at ' B ' starts running in a direction perpendicular to ' AB ' with velocity ' V ₁ '. The girl at 'A' starts running simultaneously with velocity ' V ₂ ' and in shortest distance meets the other girl in time ' t '. The value of ' t ' is

Step-by-step solution

Establish a coordinate system where girl A starts at (0,0) and girl B at (b,0) . Girl B runs perpendicular to AB with velocity V₁ , placing her position at time t at (b, V₁ t) . Girl A runs directly toward this meeting point with velocity V₂ . The distance traveled by A is the straight-line distance between initial positions, given by the Pythagorean theorem: (V₂ t)^2 = b^2 + (V₁ t)^2 Solving for t : V₂^2 t^2 - V₁^2 t^2 = b^2 t^2 (V₂^2 - V₁^2) = b^2 t = b V₂^2 - V₁^2 This solution requires V₂ > V₁ for real t . The