Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

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 $.....$

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 ...........

A bullet is fired from a gun at the speed of $280\,ms ^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $........\,m$ $\left(g=9.8\,ms ^{-2}, \sin 30^{\circ}=0.5\right):-$

A stone is thrown at an angle $\theta $ to the horizontal reaches a maximum height $H$. Then the time of flight of stone will be

The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2 \theta$. What is the value of $\theta$ ?