$A$ person can throw a ball up to a maximum range of $100 \, m$. How high above the ground can he throw the same ball (in $, m$)?

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

$A$ boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

$A$ body of mass $1 \, kg$ is projected from the ground at an angle of $30^{\circ}$ with the horizontal on level ground at a speed of $50 \, m/s$. The magnitude of the change in momentum of the body during its entire flight is ....... $kg \cdot m/s$ $(g = 10 \, m/s^2)$.

$A$ particle having kinetic energy $K$ is projected at $60^{\circ}$ with the horizontal. The kinetic energy at the highest point is

$A$ ball rolls from the top of a stairway with a horizontal velocity $u \; m/s$. If the steps are $h \; m$ high and $b \; m$ wide,the ball will hit the edge of the $n^{th}$ step,if $n=$