If the initial kinetic energy of a projectile is $100 \, J$ and the kinetic energy at the maximum height is $30 \, J$,what is the angle of projection?

$A$ particle of mass $m$ is projected with a velocity $u$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is:

The angle of projection for a projectile to have the same horizontal range and maximum height is

Two particles $A$ and $B$ are projected simultaneously from a fixed point on the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$,while particle $B$ is projected in air with speed $\frac{2v}{\sqrt{3}}$. If particle $B$ hits particle $A$,the angle of projection of $B$ with the vertical is

$A$ $1.5 \,kg$ ball is shot upward at an angle of $34^{\circ}$ to the horizontal with an initial speed of $20 \,m/s$. The maximum height reached by the ball is (use $\cos 34^{\circ} = 0.83$ and $\sin 34^{\circ} = 0.56$): (in $\,m$)

$A$ cricket ball is hit at $30^{\circ}$ with the horizontal with kinetic energy $K$. The kinetic energy at the highest point is