The velocity at the maximum height of a projectile is half of its initial velocity $u$. Its range on the horizontal plane is

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

When a body is thrown with a velocity $u$ making an angle $\theta $ with the horizontal plane, the maximum distance covered by it in horizontal direction is

A projectile is projected from ground with initial velocity $\vec u\, = \,{u_0}\hat i\, + \,{v_0}\hat j\,$. If acceleration due to gravity $(g)$  is along the negative $y-$ direction then find maximum displacement in $x-$ direction

A  particle of mass  $m$ is projected with velocity $v$ making an angle of $45^o $ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

A projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be ......... $K$