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 particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height h above $O$) with velocity $v$ at an angle of projection $\theta$ . The time when the distance between them is minimum is

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

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y=\left(4 t-2 t^2\right) m$ and $x =(3 t)$ metre, where $t$ is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is .........

An arrow is shot into air. Its range is $200\,m$ and its time of flight is $5\,s$. If $g=10\,m / s ^2$, then horizontal component of velocity and the maximum height will be respectively

A ground to ground projectile is at point $A$ at $t=\frac{T}{3}$, is at point $B$ at $t=\frac{5 T}{6}$ and reaches the ground at $t=T$. The difference in heights between points $A$ and $B$ is