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Motion In Straight Line

Question
CBSEENPH11026296

Two boys are standing at the ends A and B of a ground, where AB= a. The boy at B starts running in a direction perpendicular to AB with velocity The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

  • av2 + v12

  • a2v2 - v12

  • av - v1  

  • av + v1

Solution

B.

a2v2 - v12

Distance covered by boy A in time t

               AC = vt                            ...(i)

Distance covered by boy B in time t

            BC = v1 t                               ... (ii)

Using Pythagourus theorem

           AC2 = AB2 + BC2

           ( vt )2 = a2 + (v1 t)2         

                   

⇒          v2 t2 - v12 t2 = a2

⇒          t2  v2 - v12   = a2

⇒          t = a2v2 - v12