The angle of projection of a projectile for which its initial kinetic energy becomes half at its maximum height is (in $^{\circ}$)

$A$ particle is projected upwards with a velocity of $100 \ m/s$ at an angle of $60^{\circ}$ with the vertical. Find the time when the particle will move perpendicular to its initial direction,$.....$ seconds (take $g = 10 \ m/s^2$):-

$A$ particle aimed at a target,projected with an angle $15^{\circ}$ with the horizontal is short of the target by $10 \ m$. If projected with an angle of $45^{\circ}$ it is away from the target by $10 \ m$,then the angle of projection to hit the target is

The angle of projection at which the horizontal range and maximum height of a projectile are equal is

$A$ ball is projected with a velocity of $10 \ ms^{-1}$ at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be $............... \ ms^{-1}$.

$A$ $1.5 \,kg$ 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 $\,m$)