A ball is projected with a velocity $3\hat{i}+4\hat{j}$ m/s .  The time after which its velocity vector is normal to initial velocity vector is (g = 10 m/$s^2$)
 

when velocity becomes perpendicular to initial velocity horizontal velocity will remain same but vertical velocity changes.Let the velocity is $3\hat{i}+v\hat{j}$  as they are perpendicular their dot product will be zero.

$$\begin{gathered} \left(3\hat{i}+4\hat{j}\right).\left(3\hat{i}+v\hat{j}\right)=0 \\ 9+4v=0\Rightarrow \Rightarrow v=-\frac{9}{4}=4-gt \\ gt=4+\frac{9}{4}=\frac{25}{4} \\ t=\frac{25}{40}=0.625 \end{gathered}$$

alternate method v is perpendicular to u after t=$\frac{u}{g\sin \theta }=\frac{u^2}{gu\sin \theta }=\frac{25}{10\times 4}=0.625$