Column $-I$     Angle of projection	Column $-II$
$A.$ $\theta \, = \,{45^o}$	$1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$
$B.$ $\theta \, = \,{60^o}$	$2.$ $\frac{{g{T^2}}}{R} = 8$
$C.$ $\theta \, = \,{30^o}$	$3.$ $\frac{R}{H} = 4\sqrt 3 $
$D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$	$4.$ $\frac{R}{H} = 4$

$K_i :$ initial kinetic energy

$K_h :$ kinetic energy at the highest point

Range of a bob of mass $1\, kg$ is $80\,m$ while it attains maximum height $20\,m$. Its  change in momentum in complete motion ............ $N-s$

A fighter plane is flying horizontally at a height of $250\  m$ from ground with constant velocity of $500\  m/s$. It passes exactly over a cannon which can fire a shell at any time in any direction with a speed of  $100\  m/s$. Find the duration of time  for which the plane is in danger of being hit by a cannon shell

Range of a bullet fired at $45^o$ to horizontal is $980m$. If the bullet is fired at same  angle from a car travelling horizontally at $18\, km/hr$ towards target then range will be  increased by :-

A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \;ms ^{-1}$ and $19.6\; ms ^{-1}$. It will strike the plane after covering distance of ........ $m$

A projectile is launched at an angle ' $\alpha$ ' with the horizontal with a velocity $20 \; ms ^{-1}$. After $10 s$, its inclination with horizontal is ' $\beta$ '. The value of $\tan \beta$ will be : $\left( g =10 \; ms ^{-2}\right)$