$A$ stone is projected with kinetic energy $E$,making an angle $\theta$ with the horizontal. When it reaches its highest point,its kinetic energy is

$A$ 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 $\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]$

$A$ particle is projected in air at some angle to the horizontal and moves along a parabola as shown in the figure,where $x$ and $y$ indicate horizontal and vertical directions,respectively. The diagram shows the direction of velocity and acceleration at points $A$,$B$,and $C$.

$A$ ball is thrown at an angle $\theta$ with the horizontal. Its horizontal range is equal to its maximum height. This is possible only when the value of $\tan \theta$ is ..........

Two objects are projected with the same velocity '$u$' but at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$,the ratio of the horizontal range of the first object to the $2^{\text{nd}}$ object will be:

$A$ particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal,its speed changes to $v$,where