Two balls A and B are projected at an angle of $45^\circ$ and $60^\circ$ respectively, so that the maximum heights reached are same for both. The ratio of initial velocity of projection of ball A to that for ball B is
$(\sin 30^\circ = \cos 60^\circ = \dfrac{1}{2},\ \sin 45^\circ = \cos 45^\circ = \dfrac{1}{\sqrt{2}},\ \sin 60^\circ = \cos 30^\circ = \dfrac{\sqrt{3}}{2})$

Two objects are projected with same velocity 'u' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^\circ$, the ratio of horizontal range of the first object to the second object will be $[\sin(\pi - \theta) = \sin\theta]$

A ball is released from height 'h' which makes perfectly elastic collision with ground. The frequency of periodic vibratory motion is (g=acceleration due to gravity)

Two boys are standing at points A and B on ground where distance AB = a. The boy at point B starts running perpendicular to line AB with velocity '$V_1$'. The boy at point A starts running simultaneously with velocity 'V' and catches the other boy in time 't'. The value of 't' is