The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option:

$A$ ball is hit by a batsman at an angle of $37^o$ with an initial velocity $u = 15 \ m/s$ as shown in the figure. The man standing at $P$ is at a distance of $9 \ m$ from the point $B$ where the ball would strike the ground. What is the minimum velocity at which the man should run to catch the ball before it hits the ground? Assume the height of the man is negligible. ........ $m/s$

Three particles start simultaneously from a point on a horizontal smooth plane. The first particle moves with speed $v_1$ towards the east,the second particle moves towards the north with speed $v_2$,and the third one moves towards the north-east. The velocity of the third particle,such that the three particles always lie on a straight line,is

Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$,where $t$ is

$A$ particle of mass $m$ is projected at $45^o$ at $V_0$ speed from point $P$ at $t = 0$. The angular momentum of the particle about $P$ at $t = \frac{V_0}{g}$ is:

$A$ block of mass $5\,kg$ is moving horizontally at a speed of $1.5\,m/s$. $A$ perpendicular force of $5\,N$ acts on it for $4\,s$. What will be the distance of the block from the point where the force started acting?