Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to  horizontal, after one more second it is travelling horizontally. What is the magnitude and  direction of its velocity at initial point

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 $h = \Delta x\,\left[ {1 + \frac{{\Delta x}}{R}} \right]$.

The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45^o}$. The range will be minimum, if the angle of projection is ......... $^o$

A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \;ms ^{-1}$ and $19.6\; ms ^{-1}$. It will strike the plane after covering distance of ........ $m$

The $x-t$ graph of a particle moving along a straight line is shown in figure The speed-time graph of the particle is correctly shown by

A particle $A$ is projected vertically upwards. Another identical particle $B$ is projected at an angle of $45^o $ . Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is