A ball of mass $0.2 \ kg$ rests on a vertical post of height $5 m$. A bullet of mass $0.01 \ kg$, traveling with a velocity $V / s$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \ m$ and the bullet at a distance of $100 \ m$ from the foot of the post. The initial velocity $V$ of the bullet is

An aeroplane is flying at a constant horizontal velocity of $600\, km/hr $ at an elevation of $6\, km$ towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

A man runs across the roof, top 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 be able to land on the next building ? $($ Take $g = 10 \,m/s^2)$

The initial speed of a bullet fired from a rifle is $630\, m/s$. The rifle is fired at the centre of a target $700\, m$ away at the same level as the target. How far above the center of the target (in $m$) the rifle must be aimed in order to hit the target? (Take $g=10 \;m/s^2$)

A ball rolls off the top of a stairway with horizontal velocity $\mathrm{u}$. The steps are $0.1 \mathrm{~m}$ high and $0.1 \mathrm{~m}$ wide. The minimum velocity $\mathrm{u}$ with which that ball just hits the step $5$ of the stairway will be $\sqrt{\mathrm{x}} \mathrm{ms}^{-1}$ where $\mathrm{x}=$___________ [use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ].

A ball rolls from the top of a stair way with a horizontal velocity $u\; m /s$ . If the steps are $h\; m$ high and $b\; m$ wide, the ball will hit the edge of the $n^{th}$ step, if $n=$