A ball is hit by a batsman at an angle of $37^o$ as shown in figure. The man standing at $P$ should run at what minimum velocity so that he catches the ball before it strikes the ground. Assume that height of man is negligible in comparison to maximum height of projectile.  ........ $ms^{-1}$

A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle ' $\theta$ ' to the horizontal, the maximum height attained by it equals $4 \mathrm{R}$. The angle of projection, $\theta$, is then given by

Two particles $A$ and $B$ are moving in horizontal plane as shown in figure at $t = 0$ , then time after which $A$ will catch $B$ will be.......$s$

A ball is thrown at different angles with the same speed $u$ and from the same point. It has the same range in both cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2$ equals to

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be $.......$ degree.

An object is thrown along a direction inclined at an angle of ${45^o}$ with the horizontal direction. The horizontal range of the particle is equal to