The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2\theta$. What is the value of $\theta$ (in $^{\circ}$)?

$A$ 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.

$A$ body of mass $m$ is thrown upwards at an angle $\theta$ with the horizontal with velocity $v$. While rising up,the velocity of the mass after $t$ seconds will be:

$A$ projectile is launched from the ground, such that it hits a target on the ground which is $90 \,m$ away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)

$A$ stone is projected with kinetic energy $E$,making an angle $\theta$ with the horizontal. When it reaches its highest point,its kinetic energy is

$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight, then the value of maximum range is (acceleration due to gravity $= g$)