A ball of mass $m$ is thrown vertically upward. Another ball of mass $2\,m$ is thrown an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$

In the motion of a projectile freely under gravity, its

For angles of projection of a projectile at angle $(45^o  +\theta)$ and $(45^o  -\theta ) $ , the horizontal range described by the projectile are in the ratio of 

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second. The velocity with which the projectile is projected is ......... $m/sec$.

A projectile is thrown with velocity $v$ at an angle $\theta$ with horizontal. When the projectile is at a height equal to half of the maximum height, the vertical component of the velocity of projectile is ...........

An object is thrown along a direction inclined at an angle of ${45^o}$ with the horizontal direction. The horizontal range of the particle is equal to