Horizontal Projectile

iii) Velocity of the projectile at any time 't'

Let the body be at point P after the time t.
Let v_x and v_y be velocities along x and y-directions.
The horizontal velocity remains constant throughout the motion. Hence v_x= u.
The velocity along Y-axis is
\( v_y = u_y + gt \) and u_y= 0 as the body is thrown horizontally initially.
             \( \therefore v_y = gt \)  
      

          \( V = \sqrt {v_x^2 + v_y^2 } = \sqrt {u^2 + g^2 t^2 } \)
If velocity vector v makes an angle \(\alpha\) with the horizontal then
    \( \tan \alpha = \frac{{v_y }} {{v_x }} = \frac{{gt}} {u} \)  (or) \( \alpha = \tan ^{ - 1} \left( {\frac{{gt}} {u}} \right) \)