Ram moves in the east direction at a speed of $6 \, m/s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \, m/s$. The magnitude of their relative velocity is ........ $m/s$.

$A$ $2\,m$ wide truck is moving with a uniform speed $v_0=8\,m/s$ along a straight horizontal road. $A$ pedestrian starts to cross the road with a uniform speed $v$ when the truck is $4\,m$ away from him. The minimum value of $v$ so that he can cross the road safely is $...........\,m/s$.

Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

$A$ boat moves with a speed of $5 \, km/h$ relative to water in a river flowing with a speed of $3 \, km/h$ and having a width of $1 \, km$. The minimum time taken for a round trip is ......... $min$.

$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of the ground in $m \; s^{-1}$ with respect to train $B$?