Question

Show that trajectory of an object thrown from a certain height is parabola

Answer 1

Answer:

Trajectory of a projectile is a parabola:

   Consider a body projected with an initial velocity u at an angle   with the horizontal from O.

   The body moves along OAB and reaches the ground.

   The path OAB is called as the trajectory of a projectile.

           x = horizontal displacement

           y = vertical displacement

   'u' can be resolved into two components

           =horizontal component of velocity which is constant

                                  =

           = vertical component of velocity

                                  =

   Similarly, the components of acceleration are

           = horizontal component of acceleration = 0

           = vertical component of acceleration = ± g

   Let 't' be the time period

   Horizontal displacement is given by

         

   From equations of motion, we have

         

∴ Trajectory of a projectile is a parabola