The horizontal range of a projectile projected at an angle of $45^{\circ}$ with the horizontal is $50 \ m$. The height of the projectile when its horizontal displacement is $20 \ m$ is (in $m$)

Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at an angle of $60^\circ$ to the horizontal,the ratio of the maximum heights reached is

$A$ particle is projected in air at some angle to the horizontal and moves along a parabola as shown in the figure,where $x$ and $y$ indicate horizontal and vertical directions,respectively. The diagram shows the direction of velocity and acceleration at points $A$,$B$,and $C$.

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	$4$. $60$

Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long-jump event?

$A$ body is projected at an angle $\theta$ with the horizontal. Another body is projected with the same speed at an angle $\theta$ with the vertical. The ratio of their maximum heights is: