$A$ ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight,its kinetic energy will be

The equation of motion of a projectile is $y = ax - bx^2$,where $a$ and $b$ are constants. Match the Column-$I$ with Column-$II$:

Column-$I$	Column-$II$
$i)$ The initial velocity of projection	$a)$ $\sqrt{\frac{g(1+a^2)}{2b}}$
$ii)$ The horizontal range of projectile	$b)$ $\frac{a}{b}$
$iii)$ The maximum height attained by projectile	$c)$ $\frac{a^2}{4b}$
$iv)$ The time of flight of projectile	$d)$ $a\sqrt{\frac{2}{bg}}$

At what angle should a particle be projected to cover the maximum range (in $^{\circ}$)?

At what point of a projectile motion are acceleration and velocity perpendicular to each other?

$A$ ball is thrown upwards at an angle of $60^o$ to the horizontal. It falls on the ground at a distance of $90 \,m$. If the ball is thrown with the same initial velocity at an angle $30^o$,it will fall on the ground at a distance of ........ $m$.

$A$ body projected with some velocity at an angle $45^{\circ}$ with the horizontal from the origin in $XY$-plane passes through a point at $(4, 3) \ m$. Its horizontal range is (in $m$)