$A$ body is projected with a speed $u \ m/s$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $3/4$ of the initial kinetic energy. The value of $\beta$ is: (in $^{\circ}$)

$A$ cricket ball is thrown by a player at a speed of $20\,m/s$ in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is $........\,m$ $\left( g = 10\,m/s^2 \right)$

At the top of the trajectory of a projectile,the directions of its velocity and acceleration are

The equation of motion of a projectile is $y = Ax - Bx^2$ where $A$ and $B$ are constants of motion. The horizontal range of the projectile is

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^{\circ}$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$, where $h$ is the height, $x$ is the horizontal distance, and $A$ and $B$ are constants. The ratio $A:B$ is $(g = 10 \ m/s^2)$.

Two stones having different masses $m_1$ and $m_2$ are projected at an angle $\alpha$ and $(90^{\circ}-\alpha)$ with the same speed from the same point. The ratio of their maximum heights is