$A$ person sitting in an open car moving at a constant velocity throws a ball vertically up into the air. The ball falls:

$A$ projectile is fired at a speed of $100 \, m/s$ at an angle of $37^o$ above the horizontal. At the highest point,the projectile breaks into two parts of mass ratio $1:3$,the smaller coming to rest. Then the distance of the heavier part from the launching point is ........... $m$.

$A$ particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point:

The velocities of two particles $A$ and $B$,separated by a distance of $20 \ m$,are as shown in the figure. Find the angular velocity of $B$ with respect to $A$ in $rad/s$.

$A$ projectile is thrown with a velocity of $10\,m/s$ at an angle of $60^{\circ}$ with the horizontal. The time interval between the moments when the speed is $\sqrt{5g}\,m/s$ is $..........\,s$ (take $g=10\,m/s^2$).

$A$ person moves from $A$ to $B$ on a circular path as shown in the figure. If the distance travelled by him is $60 \, m$,then the magnitude of the displacement would be $..... \, m$. (Given $\cos 135^{\circ} = -0.7$)