A projectile is thrown into space so as to have a maximum possible horizontal range of $400$ metres. Taking the point of projection as the origin, the co-ordinates of the point where the velocity of the projectile is minimum are

The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it, will be

From the top of a tower of height $40\,m$, a ball is projected upwards with a speed of $20\,m / s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m / s ^2$ )

A shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection then the angular elevation of the summit $\beta$ is

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 boy can throw a stone up to a maximum height of $10\ m$. The maximum horizontal distance that the boy can throw the same stone up to will be ..........  $m$