motion in a plane

Question

A body is projected with a speed v₀ horizontally from the top of a tower. Find the horizontal displacement of the particle, when the magnitude of vertical component of velocity is equal to magnitude of horizontal component of velocity.

Options:

Answer 1

         Horizontal displacement =v₀t [as the acceleration is zero]

          In a horizontal projectile, horizontal velocity remains constant.

          it is given that at a certain time horizontal velocity is equal to vertical velocity

                          v_y = v₀

                      Generally,    v_y = u + gt [u = 0]

                                           v₀ = gt

                                           t =  v₀ /g ----------(1)

     As given above horizontal displacement at time t = v₀t ----------(2)

      substitute the above equation (1) in (2)

                                              s_x = v₀ (v₀ /g)

                                             s_x = v₀ ² /g