There are three steps,each with a height of $10 \, cm$ and a width of $20 \, cm$. What minimum horizontal velocity (in $m/s$) must be given to a ball from the top step so that it clears all three steps?

$A$ body is projected from the top of a tower with a velocity $\overrightarrow{u} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} \text{ m/s}$, where $\hat{i}, \hat{j},$ and $\hat{k}$ are unit vectors along east, north, and vertically upwards, respectively. If the height of the tower is $30 \text{ m}$, find the horizontal range of the body on the ground. (Take $g = 10 \text{ m/s}^2$) (in $\text{ m}$)

Shots are fired from the top of a tower and from its bottom simultaneously at angles $30^o$ and $60^o$ as shown. If the horizontal distance of the point of collision is at a distance $a$ from the tower,then the height of the tower $h$ is:

$A$ particle is dropped from a height of $20\,m$ onto horizontal ground. There is wind blowing,due to which the horizontal acceleration of the particle becomes $6\,ms^{-2}$. Find the horizontal displacement of the particle until it reaches the ground (in $m$).

$A$ man runs across the roof of a tall building and jumps horizontally with the hope of landing on the roof of the next building,which is at a lower height than the first. If his speed is $9 \, m/s$,the horizontal distance between the two buildings is $10 \, m$,and the height difference is $9 \, m$,will he be able to land on the next building? (Take $g = 10 \, m/s^2$)

$A$ hiker stands on the edge of a cliff $490 \; m$ above the ground and throws a stone horizontally with an initial speed of $15 \; m/s$. Neglecting air resistance,find the time taken by the stone to reach the ground,and the speed with which it hits the ground. (Take $g = 9.8 \; m/s^2$).