# A ball is thrown with a velocity of u making an angle θ with the horizontal. Its velocity vector normal to initial vector (u)…..

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

(a) $\displaystyle \frac{u sin\theta}{g}$

(b) $\displaystyle \frac{u }{g cos\theta}$

(c) $\displaystyle \frac{u }{g sin\theta}$

(d) $\displaystyle \frac{u cos\theta}{g}$

Sol: $\displaystyle \vec{u} = ucos\theta \hat{i} + usin\theta \hat{j}$
$\displaystyle \vec{v} = v_x\hat{i} + v_y \hat{j}$
$\displaystyle \vec{v} = ucos\theta \hat{i} + (usin\theta – gt) \hat{j}$
$\displaystyle \vec{u}.\vec{v} = 0$
$\displaystyle t = \frac{u}{g sin\theta}$