A mouse jumps off from the $15$ th floor of a high-rise building and lands $12 \,m$ from the building. Assume that, each floor is of $3 \,m$ height. The horizontal speed with which the mouse jumps is closest to ...............$km /h$

A slide with a frictionless curved surface, which becomes horizontal at its lower end,, is fixed on the terrace of a building of height $3 h$ from the ground, as shown in the figure. A spherical ball of mass $\mathrm{m}$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0=u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\overrightarrow{\mathrm{v}}$ and reaches a maximum height $h_l$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $1 / \sqrt{3}$. Which of the following statement($s$) is(are) correct?

($AV$) $\vec{u}_0=\sqrt{2 g h} \hat{x}$ ($B$) $\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$  ($C$) $\theta=60^{\circ}$  ($D$) $d / h_1=2 \sqrt{3}$

The maximum range of a gun on horizontal terrain is $16 \,km$. If $g = \;10m/{s^2}$. What must be the muzzle velocity of the shell ......... $m/s$

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 bomb is released from a horizontal flying aeroplane. The trajectory of bomb is

Two paper screens $A$ and $B$ are separated by distance $100 \,m$. A bullet penetrates $A$ and $B$, at points $P$ and $Q$ respectively, where $Q$ is $10 \,cm$ below $P$. If bullet is travelling horizontally at the time of hitting $A$, the velocity of bullet at $A$ is nearly .......... $m / s$