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

$A$ ball is thrown from a point with a speed $v_0$ at an elevation angle of $\theta$. From the same point and at the same instant,a person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes,what should be the angle of projection $\theta$?

Two stones are thrown with the same speed $u$ at different angles from the ground into the air. If both stones have the same range and the heights attained by them are $h_1$ and $h_2$,then $h_1 + h_2$ is equal to .......

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 $y = 8t - 5t^2 \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The velocity with which the projectile is projected is (in $\text{ m/s}$)

What do you mean by projectile motion and projectile particle? Find the value of the position of a projectile particle at any instant of time.

The equation of a projectile is given by $y = Px - Qx^2$,where $P$ and $Q$ are constants. The ratio of the maximum height to the range of the projectile is