$A$ gun is aimed at a target in the line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

$A$ projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range,then its kinetic energy at the highest point will be ......... $K$.

$A$ projectile is fired from level ground at an angle $\theta$ above the horizontal. The elevation angle $\phi$ of the highest point as seen from the launch point is related to $\theta$ by the relation

The path of a projectile is given by the equation $y = ax - bx^2$,where $a$ and $b$ are constants,and $x$ and $y$ are the horizontal and vertical distances of the projectile from the point of projection,respectively. The maximum height attained by the projectile and the angle of projection are respectively:

$A$ projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3 \, ms^{-2}$ for $0.5 \, minutes$. If the maximum height reached by it is $80 \, m$,then the angle of projection is (Take $g = 10 \, ms^{-2}$)

The initial velocity of a particle of mass $2\,kg$ is $(4 \hat{i} + 4 \hat{j})\,m/s$. $A$ constant force of $-20 \hat{j}\,N$ is applied on the particle. Initially,the particle was at $(0,0)$. Find the $x$-coordinate of the point where its $y$-coordinate is again zero. $..........\,m$