$A$ particle is projected from the ground with a kinetic energy $E$ at an angle of $60^{\circ}$ with the horizontal. Its kinetic energy at the highest point of its motion will be

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$,where $\alpha$ and $\beta$ are constants and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by:

Two stones having different masses $m_1$ and $m_2$ are projected at an angle $\alpha$ and $(90^{\circ}-\alpha)$ with the same speed from the same point. The ratio of their maximum heights is

The maximum horizontal range of a projectile is $400\, m$. The maximum height attained by it will be ......... $m$.

$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $150\, ms^{-1}$. Then the time after which its inclination with the horizontal is $45^{\circ}$ is

The velocity of a projectile is $(6\hat{i} + 8\hat{j}) \ m/s$. Its horizontal range is ........ $m$.