Two particles $A$ and $B$ are moving in horizontal plane as shown in figure at $t = 0$ , then time after which $A$ will catch $B$ will be…….$s$

An object is thrown along a direction inclined at an angle of ${45^o}$ with the horizontal direction. The horizontal range of the particle is equal to

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

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 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