$A$ stone is projected with a velocity $20 \sqrt{2} \, m/s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of the stone during its motion from the starting point to its maximum height is $.......... \, m/s$ (take $g = 10 \, m/s^2$).

$A$ particle of mass $m$ is projected at a velocity $u$, making an angle $\theta$ with the horizontal ($x$-axis). If the angle of projection $\theta$ is varied keeping all other parameters same, then the magnitude of angular momentum $(L)$ at its maximum height about the point of projection varies with $\theta$ as,

The displacement vector of a particle of mass $m$ is given by $\vec{r}(t) = A \cos \omega t \hat{i} + B \sin \omega t \hat{j}$.
$(a)$ Show that the trajectory is an ellipse.
$(b)$ Show that $\vec{F} = -m \omega^2 \vec{r}$.

Balls $A$ and $B$ are thrown from two points lying on the same horizontal plane separated by a distance of $120\,m$. Which of the following statement$(s)$ is/are correct?

$A$ projectile has the same range $R$ for two angles of projection. If $T_1$ and $T_2$ are the times of flight in the two cases,then $R$ is

The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be: