A projectile is fired at $30^{\circ}$ to the horizontal, The vertical component of its velocity is $80 \;ms ^{-1}$, Its time flight is $T$. What will be the velocity of projectile at $t =\frac{ T }{2}$?

A ball thrown by one player reaches the other in $2\, sec$. The maximum height attained by the ball above the point of projection will be about .......... $m$

The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45^o}$. The range will be minimum, if the angle of projection is ......... $^o$

A projectile is fired with a velocity at right angle to the slope which is inclined at an angle $\theta$ with the horizontal. The expression for the range $R$ along the incline is

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m / s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\frac{m}{s}$

Two particles $A$ and $B$ are projected simultaneously from a fixed point of the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$, while particle $B$ is projected in air with speed $\frac{2 v}{\sqrt{3}}$. If particle $B$ hits the particle $A$, the angle of projection of $B$ with the vertical is