$A$ particle having kinetic energy $K$ is projected at $60^{\circ}$ with the horizontal. The kinetic energy at the highest point is

$A$ particle $P$ is projected with velocity $u_1$ at an angle of $30^\circ$ with the horizontal. Another particle $Q$ is projected vertically upwards with velocity $u_2$ from the point directly below the maximum height of $P$. The condition for the collision of both particles is:

$A$ ball is thrown upwards and it returns to the ground describing a parabolic path. Which of the following remains constant?

$A$ projectile is thrown at an angle $\theta$ with the horizontal and its range is $R_1$. It is then thrown at an angle $\theta$ with the vertical and the range is $R_2$. Then:

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is:

$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.