Question

Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by 

θ (t)= tan^-1(v_oy-gt/v_ox)

Show that the projection angle θ₀  for a projectile launched from the origin is given by

θ_{0 =tan^-1(4hm/R)}

Where the symbols have their usual meaning.

Answer 1

Let v_ox andv_oy respectively be the initial components of the velocity of the projectile along horizontal (x) and vertical (y) directions.

Let v_x and v_y respectively be the horizontal and vertical components of velocity at a point P.

Time taken by the projectile to reach point P = t
Applying the first equation of motion along the vertical and horizontal directions, we get: