From the ground level, a ball is to be shot with a certain speed. Graph shows the range $(R)$ of the particle versus the angle of projection from horizontal ( $\theta $ ). Values of $\theta _1$ and $\theta _2$ are

The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection $(u)$. Its range on the horizontal plane is ………….

A cricketer can throw a ball to a maximum horizontal distance of $100\, m$. The speed with which he throws the ball is   ……… $ms^{-1}$ (to the nearest integer)

Two bodies are thrown up at angles of $45^o $ and $60^o $, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

A particle is projected from the ground with an initial speed $\upsilon $ at an angle $\theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is