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 height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second. The velocity with which the projectile is projected is ......... $m/sec$.

Shots are fired from the top of a tower and from its bottom simultaneously at angles $30^o$ and $60^o$ as shown. If horizontal distance of the point of collision is at a distance $'a'$ from the tower then height of tower $h$ is :

A cricketer hits a ball with a velocity $25\,\,m/s$ at ${60^o}$ above the horizontal. How far above the ground it passes over a fielder $50 m$ from the bat  ........ $m$ (assume the ball is struck very close to the ground)

For angles of projection of a projectile at angle $(45^o  +\theta)$ and $(45^o  -\theta ) $ , the horizontal range described by the projectile are in the ratio of 

A ball is projected with kinetic energy $E$ at an angle of ${45^o}$ to the horizontal. At the highest point during its flight, its kinetic energy will be