$A$ boy weighing $50 \ kg$ finished a long jump at a distance of $8 \ m$. Considering that he moved along a parabolic path and his angle of jump is $45^{\circ}$,his initial $K.E.$ is (in $J$)

$A$ ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1 \ m$ high and $0.1 \ m$ wide. The minimum velocity $u$ with which the ball just hits the $5^{\text{th}}$ step of the stairway will be $\sqrt{x} \ ms^{-1}$ where $x=$ . . . . . . [use $g=10 \ ms^{-2}$].

An aeroplane flying at a constant velocity releases a bomb. As the bomb drops down from the aeroplane,

Two projectiles are projected with the same initial velocities at $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

The equation of trajectory of a projectile is $y = 10x - (5/9)x^2$. If we assume $g = 10 \ m/s^2$, the range of the projectile (in meters) is:

On a planet, a particle is thrown with a velocity $\vec{V} = 6 \hat{i} + (20 - 4t) \hat{j}$. Match the lists. (All quantities are in $SI$ units)

$P$. Time of flight	$1$. $3$
$Q$. Time when particle is moving at an angle of $53^{\circ}$ with horizontal in upwards direction	$2$. $10$
$R$. Range of the particle	$3$. $50$
$S$. Maximum height reached by the particle	$4$. $60$