$A$ stone is projected from the ground with velocity $25\,m/s$. Two seconds later,it just clears a wall $5\,m$ high. The angle of projection of the stone is ........ $^o$ $(g = 10\,m/s^2)$.

$A$ particle of mass $m$ is projected with a velocity $V$ making an angle of $45^{\circ}$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is

Galileo,in his book $Two \text{ } new \text{ } sciences$,stated that "for elevations which exceed or fall short of $45^{\circ}$ by equal amounts,the ranges are equal". Prove this statement.

$A$ particle is projected from the ground with a speed of $80 \,m/s$ at an angle of $30^{\circ}$ with the horizontal. The magnitude of the average velocity of the particle in the time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m/s$. (Take $g=10 \,m/s^2$)

$A$ particle is projected from the ground with a kinetic energy $E$ at an angle of $60^{\circ}$ with the horizontal. Its kinetic energy at the highest point of its motion will be

The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it,$P$ is equal to