$A$ projectile is thrown with an initial velocity $(a \hat{i} + b \hat{j}) \ m/s$,where $\hat{i}$ and $\hat{j}$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it,then

$A$ 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 ............... $km/h$.

For a projectile,the maximum height and horizontal range are same. The angle of projection $\theta$ of the projectile is

$A$ particle is projected with velocity $2 \sqrt{gh}$,so that it just flies over two walls of equal height $h$ and $2h$ distance apart from each other. Find the time for which the particle flies between the walls.

$A$ ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant,a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes,what should be the angle of projection?

The height of the ceiling in an auditorium is $30 \ m$. $A$ ball is thrown with a speed of $30 \ m \ s^{-1}$ from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of the auditorium is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)