The horizontal range of a projectile is $4\sqrt 3 $ times its maximum height. Its angle of projection will be    ......... $^o$

A person is standing on an open car moving with a constant velocity of $30\,\,m/s$  on a straight horizontal road. The man throws a ball in the vertically upward direction and it returns to the person after the car has moved $240\,\,m.$  The speed and the angle of projection

A stone is projected from the ground with velocity $50 \,m/s$ at an angle of ${30^o}$. It crosses a wall after $3$ sec. How far beyond the wall the stone will strike the ground ..........  $m$ $(g = 10\,m/{\sec ^2})$

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

A gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R_{max} = \frac {v_0^2}{g}$.  If a target farther away by distance $\Delta x$ (beyond $R$) has to be hit with the same gun, show that it could be achieved by raising the gun to a height at least $h = \Delta x\,\left[ {1 + \frac{{\Delta x}}{R}} \right]$.

A projectile is thrown into space so as to have a maximum possible horizontal range of $400$ metres. Taking the point of projection as the origin, the co-ordinates of the point where the velocity of the projectile is minimum are