A particle is projected from ground at some angle with the horizontal. Let $P$ be the point at maximum height $H$. At what height above the point $P$ should the particle be aimed to have range equal to maximum height?

Q. A particle is projected under gravity with velocity $\sqrt{2ag}$ from a point at a height $h$ above the level plane at an angle $\theta$ to it. The maximum range $R$ on the ground is

Q. A particle is projected under gravity with velocity $\sqrt{2ag}$ from a point at a height $h$ above the level plane at an angle $\theta$ to it. The maximum range $R$ on the ground is $\frac{x\sqrt{a(a+h)}}{4}$. Find $x$

Q. A particle is projected upwards with some velocity. At what height from ground should another particle be just dropped at the same time so that both reach the ground simultaneously. Assume that first particle reaches to a maximum height $H$.

Q.

A particle is projected from point A on the ground at an angle $\theta$ with horizontal. Another particle is projected from point B simultaneously from height 4H above point A with same velocity. A and B are in the same vertical plane, where H is the maximum height attained by the particle A. Both the particles collide at the same time on the ground. Find the angle at which particle B is projected with horizontal:

Q.

A particle is projected with an initial speed u form a point at height h above the horizontal plane as shown is the fig. Find the maximum range on the horizontal plane