$A$ ball rolls from the top of a stairway 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 $n=$

$A$ particle is projected from the ground with an initial speed of $v$ at an angle of projection $\theta$. The average velocity of the particle between its time of projection and the time it reaches the highest point of its trajectory is

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

If the velocity at the maximum height of a projectile projected at an angle of $45^{\circ}$ is $20 \,m \,s^{-1}$, then the maximum height reached by the projectile is (Acceleration due to gravity $=10 \,m \,s^{-2}$ ) (in $\,m$)

$A$ helicopter flying horizontally with a velocity of $288 \ km/h$ drops a bomb. If the line joining the point of dropping the bomb and the point where the bomb hits the ground makes an angle $45^{\circ}$ with the horizontal, then the height at which the bomb was dropped is (Acceleration due to gravity $= 10 \ m/s^2$) (in $m$)

The equation of motion of a projectile is $y = 12x - \frac{5}{9}x^2$. The horizontal component of velocity is $3 \ ms^{-1}$. Given that $g = 10 \ ms^{-2}$,the range of the projectile is .......... $m$.