Oblique Projectile From Inclined Surface

MOTION PARAMETERS OF A PROJECTILE

i) Time of ascent (t_a)
For a projectile the time to reach maximum height is called time of ascent.
For a projectile, the vertical component of velocity v_y , is zero at the highest point.
       v_y = u sin\(\theta\) -gt,
   Here,v_y= 0 and t=t_a
        \( \therefore t_a = \frac{{u\sin \theta }} {g} = \frac{{u_y }} {g} \)  

ii) Time of flight (T):
For a projectile, the total time to reach the same horizontal plane of projection is called the time of flight. It is the total time for which the projectile remains in air.
                \( y = (u\sin \theta )t - \frac{1} {2}gt^2 \)
        Here, t=T, y = 0
          \( \therefore 0 = (u\sin \theta )T - \frac{1} {2}gT^2 \)
              \(\therefore T = \frac{{2u\sin \theta }} {g} = \frac{{2u_y }} {g} \)

Note : Time of descent =time of ascent =\( \frac{{\mathbf{time}\text{ }\mathbf{of}\text{ }\mathbf{flight}}} {2} \)