A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to

A wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is

A particle is projected at $60^o $ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is

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.  ........ $ms^{-1}$

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is ......... $^o$

A piece of marble is projected from earth's surface with velocity of $19.6 \sqrt{2}\,m / s$ at $45^{\circ}.$ $2\,s$ later its velocity makes an angle $\alpha$ with horizontal, where $\alpha$ is $..........$