Two balls of same mass are projected with the same speed, one vertically upwards and the other at an angle of $60^{\circ}$ with the vertical. The ratio of their potential energies at the highest point is:

$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is:

$A$ particle performs uniform circular motion with an angular momentum $L$. If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes

An object is projected with kinetic energy $K$ from a point $A$ at an angle $60^{\circ}$ with the horizontal. In the absence of air friction, what is the ratio of the difference in kinetic energies at points $B$ and $C$ to the kinetic energy at point $A$ (see figure)?

$A$ particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$,where the value of $n$ is (Given $g$ is the acceleration due to gravity).