$A$ bomber plane moves horizontally with a speed of $500\, m/s$ and a bomb released from it strikes the ground in $10\, s$. The angle at which it strikes the ground is $(g = 10\, m/s^2)$.

Two objects are located at a height of $10 \ m$ above the ground. At some point in time,the objects are thrown with an initial velocity of $2 \sqrt{2} \ m \ s^{-1}$ at an angle of $45^{\circ}$ and $135^{\circ}$ with the positive $X$-axis,respectively. Assuming $g = 10 \ m \ s^{-2}$,the velocity vectors will be perpendicular to each other at a time equal to: (in $s$)

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

$A$ child stands on the edge of a cliff $10 \ m$ above the ground and throws a stone horizontally with an initial speed of $5 \ m/s$. Neglecting air resistance,the speed with which the stone hits the ground will be $.......... \ m/s$ (given,$g = 10 \ m/s^2$).

$A$ boy playing on the roof of a $10 \, m$ high building throws a ball with a speed of $10 \, m/s$ at an angle $30^{\circ}$ with the horizontal. How far from the throwing point will the ball be at the height of $10 \, m$ from the ground (in $, m$)? $(g = 10 \, m/s^2, \sin 30^{\circ} = 1/2, \cos 30^{\circ} = \sqrt{3}/2)$

$A$ block starts from rest at the top of a frictionless slide at a height $h_1$ above the ground. The block leaves the slide moving perfectly horizontally at a height $h_2$ above the ground. The block eventually hits the ground travelling at an angle $\theta = 30^\circ$ below the horizontal. Then: