$A$ projectile fired with initial velocity $u$ at an angle $\theta$ has a range $R$. If the initial velocity is doubled at the same angle of projection,then the new range will be:

$A$ stone projected from the ground with a velocity $50 \ m/s$ at an angle of $30^{\circ}$ with the horizontal crosses a wall after a time of $3 \ s$. Then the horizontal distance beyond the wall that the stone strikes the ground is (acceleration due to gravity $g = 10 \ m/s^2$) (in $m$)

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

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

The vertical displacement ($y$ in metre) of a projectile in terms of its horizontal displacement ($x$ in metre) is given by $y = (\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity $g = 10 \ ms^{-2}$)

Two paper screens $A$ and $B$ are separated by a distance of $100 \,m$. $A$ bullet penetrates $A$ and $B$ at points $P$ and $Q$ respectively,where $Q$ is $10 \,cm$ below $P$. If the bullet is travelling horizontally at the time of hitting $A$,the velocity of the bullet at $A$ is nearly .......... $m/s$.