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

A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$  Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,

In dealing with motion of projectile in air, we ignore effect of air resistance on motion. This give trajectory as a parabola as you have studied. What would the trajectory look like if air resistance is include ? Sketch such a trajectory and explain why you have drawn it that way.

A cricket fielder can throw the cricket ball with a speed $v_{0} .$ If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, find

$(a)$ the effective angle to the horizontal at which the ball is projected in air as seen by a spectator

$(b)$ what will be time of flight?

$(c)$ what is the distance (horizontal range) from the point of projection at which the ball will land ?

$(d)$ find $\theta$ at which he should throw the ball that would maximise the horizontal range as  found in $(iii)$.

$(e)$ how does $\theta $ for maximum range change if $u > u_0$. $u =u_0$ $u < v_0$ ?

$(f)$ how does $\theta $ in $(v)$ compare with that for $u=0$ $($ i.e., $45^{o})$ ?

A fighter plane flying horizontally at an altitude of $1.5\; km$ with speed $720\; km / h$ passes directly overhead an anti-atrcraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed $600\; m s ^{-1}$ to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take $g=10 \;m s ^{-2}$ ).