$A$ small object slides down with initial velocity equal to zero from the top of a smooth hill of height $H$. The other end of the hill is horizontal and is at height $\frac{H}{2}$ as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is

$A$ particle is dropped from a height of $20\,m$ above horizontal ground. Due to wind,the particle experiences a constant horizontal acceleration of $6\,m/s^2$. Find the horizontal displacement of the particle when it reaches the ground.

An aeroplane is flying in a horizontal direction with a velocity of $540 \ km/h$ at a height of $1960 \ m$. When it is vertically above the point $A$ on the ground,a body is dropped from it. The body strikes the ground at point $B$. The distance $AB$ is equal to $(g = 9.8 \ m/s^2)$ (in $m$)

$A$ ball is projected from the top of a tower with a velocity of $5 \, m/s$ at an angle of $53^o$ to the horizontal. Its speed when it is at a height of $0.45 \, m$ from the point of projection is ........ $m/s$.

$A$ 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 $\text{ m}$)

$A$ stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height $h$ and then attain a maximum height $2h$ above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending,then the ratio of the speed of the bird to the horizontal speed of the stone is