$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The maximum height of the projectile is ........ $m$.

$A$ particle aimed at a target, projected with an angle $15^{\circ}$ with the horizontal is short of the target by $10 \ m$. If projected with an angle of $45^{\circ}$ it is away from the target by $10 \ m$, then the angle of projection to hit the target is

$A$ projectile is thrown with velocity $u$ making an angle $\theta$ with the vertical. It just crosses the tops of two poles each of height $h$ after $1\,s$ and $3\,s$,respectively. The maximum height of the projectile is ............ $m$.

$A$ ball is thrown from a point with a speed $v_0$ at an elevation angle of $\theta$. From the same point and at the same instant,a person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes,what should be the angle of projection $\theta$?

If the time of flight of a bullet over a horizontal range $R$ is $T$,then the angle of projection with the horizontal is ......

The horizontal range $(R)$ of a projectile is $n$ times its maximum height $(H)$. Find the angle of projection $(\theta_0)$.