Two projectiles are thrown with the same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal,respectively. The ratio of their respective ranges will be:

$A$ ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight,its kinetic energy will be

The maximum horizontal range of a projectile is $16 \ km$. When the projectile is thrown at an elevation of $30^o$ from the horizontal,it will reach a maximum height of ....... $km$.

Two objects are projected with same velocity '$u$' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$, the ratio of horizontal range of the first object to the second object will be $[\sin(\pi - \theta) = \sin \theta]$

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 $y = 8t - 5t^2 \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The velocity with which the projectile is projected is (in $\text{ m/s}$)

$A$ stone is projected vertically upwards with speed '$v$'. Another stone of same mass is projected at an angle of $60^{\circ}$ with the vertical with the same speed '$v$'. The ratio of their potential energies at the highest points of their journey is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]$