In a projectile motion,the velocity at maximum height is:

Three projectiles $A, B$ and $C$ are projected at an angle of $30^{\circ}, 45^{\circ}, 60^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are the ranges of $A, B$ and $C$ respectively,then (velocity of projection is the same for $A, B$ and $C$):

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways,then the product $t_1 t_2$ is proportional to

The equation of motion of a projectile is $y = 12x - \frac{5}{9}x^2$. The horizontal component of velocity is $3 \ ms^{-1}$. Given that $g = 10 \ ms^{-2}$,the range of the projectile is .......... $m$.

The equation of a projectile is $y = 16x - \frac{5x^2}{4}$. The horizontal range is .......... $m$.

$A$ 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