Balls $A$ and $B$ are thrown from two points lying on the same horizontal plane separated by a distance of $120\,m$. Which of the following statement$(s)$ is/are correct?

$A$ 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?

$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its

$A$ ball of mass $1 \; kg$ is thrown vertically upwards and returns to the ground after $3 \; s$. Another ball,thrown at $60^{\circ}$ with the vertical,also stays in the air for the same time before it touches the ground. The ratio of the two maximum heights reached is:

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

The figure shows a sphere of mass $500 \ g$ moving in a steady flow of air in the $x$-direction. The air-stream exerts an essentially constant force of $0.9 \ N$ on the sphere in the $x$-direction. If at $t = 0$ the sphere is moving as shown in the figure,determine the time required for the sphere to cross the $y$-axis again in $\sec$. (in $.66$)