$A$ ball $A$ is projected vertically upwards with a certain initial speed $u$. Another ball $B$ of the same mass is projected at an angle of $30^{\circ}$ with the vertical with the same initial speed $u$. At the highest point,the ratio of the potential energy of ball $A$ to that of ball $B$ will be: $(\sin 90^{\circ}=1, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}, \sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2})$

For a projectile motion, the range $R$ is '$n$' times the maximum height $H$. So the angle of projection is

$A$ projectile is given an initial velocity of $\hat{i}+2 \hat{j} \,ms^{-1}$. The Cartesian equation of its path is ($x$ and $y$ are in metres and $g=10 \,ms^{-2}$)

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body thrown horizontally from the top of the tower $A$ with a velocity $20 \ ms^{-1}$ towards the tower $B$ hits the ground at point $P$,and another body thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards the tower $A$ hits the ground at point $Q$. If a car starting from rest from $P$ reaches $Q$ in $10 \ s$,then the acceleration of the car is (acceleration due to gravity $g = 10 \ ms^{-2}$): (in $ms^{-2}$)

$A$ boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved $100 \,m$. If the truck is moving horizontally along a straight line with a constant speed $30 \,m/s$, at what speed (relative to the truck) must the projectile be thrown? (Assume $g = 10 \,m/s^2$)

$A$ body is projected with a velocity $(\hat{i} + 2\hat{j}) \text{ ms}^{-1}$,where $\hat{i}$ is along the horizontal and $\hat{j}$ is vertically upward. Then the equation of its trajectory is $(g = 10 \text{ ms}^{-2})$.