A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y=\left(4 t-2 t^2\right) m$ and $x =(3 t)$ metre, where $t$ is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is ………

Three identical balls are projected with the same speed at angle $30^o, 45^o$ and $60^o$. Their ranges are $R_1 R_2$ and $R_3$ respectively. Then

Galileo writes that for angles of projection of a projectile at angles $(45 + \theta )$ and $(45 – \theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45)$

A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time period is