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

The equation of trajectory of a projectile is $y = 10x - (5/9)x^2$. If we assume $g = 10 \ m/s^2$, the range of the projectile (in meters) is:

$A$ small ball is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity of $2 \sqrt{2} \ m/s$. The magnitude of the mean velocity averaged over the first $2 \ s$ is (take acceleration due to gravity $g = 10 \ m/s^2$). (in $m/s$)

$A$ projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle $\alpha$ with the horizontal is

Assume that the acceleration due to gravity on the surface of the moon is $0.2$ times the acceleration due to gravity on the surface of the earth. If $R_e$ is the maximum range of a projectile on the earth's surface,what is the maximum range on the surface of the moon for the same velocity of projection (in $,R_e$)?

$A$ body of mass $m$ is thrown upwards at an angle $\theta$ with the horizontal with velocity $v$. While rising up,the velocity of the mass after $t$ seconds will be: