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. $..........\,m$

In the climax of a movie,the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After some time,when they are at the same horizontal level,the villain fires a bullet horizontally towards the hero. Both the hero and the villain are falling with a constant downward acceleration of $2\ m/s^2$ due to their parachutes. Assuming the hero is within the range of the bullet and air resistance on the bullet is negligible,which of the following is correct?

The angle of projection for a projectile to have the same horizontal range and maximum height is

$A$ batsman hits a ball with a velocity '$v$',making an angle of $60^{\circ}$ with the vertical. After some time, the direction of velocity makes an angle of $60^{\circ}$ with the horizontal. The speed of the ball at this instant is $[\cos(60^{\circ}) = \frac{1}{2}, \cos(30^{\circ}) = \frac{\sqrt{3}}{2}]$.

$A$ cricket ball is hit at $30^{\circ}$ with the horizontal with kinetic energy $K$. The kinetic energy at the highest point is

$A$ ball is projected in a manner such that its horizontal range is $n$ times the maximum height. Find the ratio of potential energy to kinetic energy at the maximum height.