In the figure shown,find the velocity of the particle at point $P$ $(g = 10\,m/s^2)$.

An airplane is flying at a height of $490 \, m$ with a horizontal velocity of $60 \, km/h$. When the airplane is exactly above point $A$,a package is dropped from it. At what distance from point $A$ will the package hit the ground (in $/3 \, m$)? $(g = 9.8 \, m/s^2)$

$A$ body is projected horizontally with a velocity of $4\,m/s$ from the top of a high tower. The velocity of the body after $0.7\,s$ is nearly $.....\,m/s$ (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 $g = 9.8 \; m/s^2$).

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_{0}$ from the top of a tall tower and experience a drag force of $-kv$ $(k > 0)$,where $v$ is the instantaneous velocity. Then,

$A$ 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