$A$ $2 \ kg$ 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:

Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?

$A$ particle is moving in $x-y$ plane according to $\vec{r} = b \cos \omega t \hat{i} + b \sin \omega t \hat{j}$, where $\omega$ is a constant. Which of the following statement$(s)$ is/are true?

$A$ shot is fired from a point at a distance of $200 \ m$ from the foot of a tower $100 \ m$ high,such that it just passes over it. The direction of the shot with respect to the horizontal is (in $^{\circ}$)

$A$ projectile is projected at an angle of $30^{\circ}$ from the horizontal with an initial velocity $u$. If the range of the projectile is $R$,what will be the range if the projectile is projected at an angle of $60^{\circ}$ with the same initial velocity?

There are two points $P$ and $Q$ on a projectile path with velocities $v_P$ and $v_Q$ respectively,such that $v_P$ is perpendicular to $v_Q$. If $\alpha$ is the angle that $v_P$ makes with the horizontal at point $P$,find the correct option.