$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

Two trains, each $30 \,m$ long, are travelling in opposite directions with velocities $5 \,m/s$ and $10 \,m/s$. They will cross each other after: (in $\,s$)

$A$ man walking along a straight line with a velocity $6 \text{ km/h}$ encounters rain falling vertically down with a velocity $6\sqrt{3} \text{ km/h}$. At what angle should the man hold his umbrella to protect himself from the rain?

Train $A$ and train $B$ are running on parallel tracks in opposite directions with speeds of $36 \, km/h$ and $72 \, km/h$,respectively. $A$ person is walking in train $A$ in the direction opposite to its motion with a speed of $1.8 \, km/h$. The speed (in $m/s$) of this person as observed from train $B$ will be close to:
(take the distance between the tracks as negligible) (in $.5$)

$A$ particle $(A)$ moves due north at $3\,km/h$ and another particle $(B)$ moves due west at $4\,km/h$. The relative velocity of $A$ with respect to $B$ is $(\tan 37^{\circ} = 3/4)$.

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 $B$?