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. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where $g = $ acceleration due to gravity)

A projectile is thrown with speed $40 \,ms ^{-1}$ at angle $\theta$ from horizontal. It is found that projectile is at same height at $1 \,s$ and $3 \,s$. What is the angle of projection?

A stone is projected from the ground with velocity $25\,m/s$. Two seconds later, it just clears a wall $5 \,m$ high. The angle of projection of the stone is ........ $^o$ $(g = 10m/{\sec ^2})$

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is  .......... $^o$

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^o$ with the horizontal. At the highest point, the ratio of their potential energies is