The horizontal and vertical displacements of a projectile at time $t$ are $x=36 t$ and $y=48 t-4.9 t^2$,respectively. Initial velocity of the projectile in $m/s$ 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	$4$. $60$

The maximum horizontal range of a projectile is $400\;m$. What is the maximum height attained by it (in $;m$)?

The maximum vertical height to which a man can throw a ball is $136\,m$. The maximum horizontal distance up to which he can throw the same ball is $.....\,m$.

The maximum height attained by a projectile is increased by $10\,\%$ by increasing its speed of projection,without changing the angle of projection. The percentage increase in the horizontal range will be $...........\,\%$

$A$ small ball is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity of $2 \sqrt{2} \ m/s$. The magnitude of the mean velocity averaged over the first $2 \ s$ is (take acceleration due to gravity $g = 10 \ m/s^2$). (in $m/s$)