A ball of mass $m$ is thrown vertically upward. Another ball of mass $2\,m$ is thrown an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$

A ball is projected with kinetic energy $E$ at an angle of ${45^o}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

A projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

Three balls of same masses are projected with equal speeds at angle $15^{\circ}, 45^{\circ}, 75^{\circ}$, and their ranges are respectively $R_1, R_2$ and $R_3$, then

There are two points $P$ and $Q$ on a projectile with velocities $v_P$ and $v_Q$ respectively such that $v_P$ is perpendicular to $v_Q$ and $\alpha$ is the angle that $v_P$ makes with horizontal at point $P$. Find the correct option

Derive the formula for Range of a projectile $(R)$. Derive the formula for maximum projectile.