Two boys are standing at points A and B on ground, where distance A B=x . The boy at B stars running perpendicular to A B with velocity V₁ . The boy at A starts running simultaneously with velocity v and meets the other boy in time t . The value of t is

Step-by-step solution

Let the initial position of boy A be the origin (0,0) and boy B be at (x,0) , with boy B running perpendicular to AB with velocity V₁ . At time t , boy B's position is given by (x, V₁ t) , while boy A's position is (v_x t, v_y t) . For the boys to meet, their positions must be equal: (v_x t, v_y t) = (x, V₁ t) , yielding v_x = x/t and v_y = V₁ . The magnitude constraint v^2 = v_x^2 + v_y^2 becomes v^2 = (x/t)^2 + V₁^2 . Solving for t gives t^2 = x^2/(v^2 - V₁^2) , requiring v > V₁ for real values. The expression ma