From $18 \text{ m}$ height above the ground, a ball is dropped from rest. The height above the ground at which the magnitude of velocity equals the magnitude of acceleration (in the same set of units) due to gravity is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$ and neglect the air resistance)

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground is $n$ times that taken by it to reach the highest point of its path. The relation between $H, u$ and $n$ is:

$A$ ball is thrown vertically upward. It has a speed of $10 \; m/s$ when it has reached one-half of its maximum height. How high does the ball rise? (Take $g = 10 \; m/s^2$)

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes $t_2$ time to reach the ground from point $B$,then the height of point $B$ from the ground is

$A$ body dropped from the top of a tower clears $7/16$ of the total height of the tower in its last second of flight. The time taken by the body to reach the ground is........$s$

$A$ player throws a ball upwards with an initial speed of $29.4\; m s^{-1}$. Choose the $x=0\; m$ and $t=0\; s$ to be the location and time of the ball at its highest point. Let the vertically downward direction be the positive direction of the $x$-axis. Determine the signs of position,velocity,and acceleration of the ball during its upward and downward motion.