A stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height $h$ and then attain a maximum height $2 h$ above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending, then the ratio of the speed of the bird to the horizontal speed of the stone is

A particle is projected from a horizontal plane ($x-z$ plane) such that its velocity vector at time t is given by $\vec V = a\hat i + (b – ct)\hat j$ Its range on the horizontal plane is given by

The velocity at the maximum height of a projectile is half of its initial velocity $u$. Its range on the horizontal plane is

A stone projected with a velocity u at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity u at an angle $\left( {\frac{\pi }{2} – \theta } \right)$ with the horizontal, it reaches maximum height $ H_2$. The relation between the horizontal range R of the projectile, $H_1$ and $H_2$ is

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