$A$ $2 \ kg$ ball is thrown vertically upward and another $3 \ kg$ ball is projected with a certain angle $(\theta \neq 90^{\circ})$. Both have the same time of flight. The ratio of their maximum heights is:

$A$ plane starts its flight in a direction $\theta$ with the runway. If the distance covered by it in both horizontal and vertical directions is $600\, m$,then find $\theta$. (in $^{\circ}$)

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$,the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ as a function of time is best represented by:

$A$ particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y \hat{i} + 2x \hat{j})$,where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

$A$ particle is moving in the $xy$-plane in a circular path with its center at the origin. If at an instant the position of the particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$,then the velocity of the particle is along .......