A ball is thrown with velocity u making an angle$\theta$ with the horizontal. Its velocity vector is normal to initial velocity (u) vector after a time interval of

A body is projected with velocity = u

Angle of projection $=\theta$

After time = t

Velocity vector$\overrightarrow{v}=u\cos \theta \hat{i}+\left(\text{u}\sin \theta -\text{gt}\right)\hat{j}$

Initial velocity vector$\overrightarrow{u}=u\cos \theta \hat{i}+\text{u sin}\theta \hat{j}$

$\overrightarrow{v}.\overrightarrow{u}=0$

${\text{u}}^2{\cos }^2\theta =\left(\text{u}\sin \theta -\text{gt}\right)\text{u}\sin \theta =0$

${\text{u}}^2{\cos }^2\theta +\text{u}{\sin }^2\theta -\text{ugt}\sin \theta =0$

${\text{u}}^2=\text{ugt}\sin \theta$

$\therefore \text{t}=\frac{\text{u}}{\text{g}\sin \theta }$