A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is :

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi /3$ and its maximum height is $h_1$ then the maximum height of the other will be

Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^o , 30^o , 45^o $  and $60^o $ with the horizontal respectively. The body having shortest range is

The horizontal range of a projectile is $4\sqrt 3 $ times its maximum height. Its angle of projection will be    ......... $^o$

A ball thrown by one player reaches the other in $2$ sec. the maximum height attained by the ball above the point of projection will be about ....... $m$