Two guns $A$ and $B$ can fire bullets at speed $1\, km/s$ and $2\, km/s$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is
$1:16$
$1:2$
$1:4$
$1:8$
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 $n=$
A fighter jet is flying horizontally at a certain altitude with a speed of $200 \; ms ^{-1}$. When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is $400 \; m / s$, the value of $\theta$ will be $\dots \; {}^o$
A body of mass $M$ thrown horizontally with velocity $v$ from the top of the tower of height $\mathrm{H}$ touches the ground at a distance of $100 \mathrm{~m}$ from the foot of the tower. A body of mass $2 \mathrm{M}$ thrown at a velocity $\frac{v}{2}$ from the top of the tower of height $4 \mathrm{H}$ will touch the ground at a distance of. . . . ..
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 $g = 10 \,m/s^2)$