$A$ person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5\, m/s$ at an angle of $120^\circ$ with the direction of flow of water. The speed of water in the stream is..........$m/s$.

$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

$A$ boat crossing a river moves with a velocity $v$ relative to still water. The river is flowing with a velocity $v/2$ with respect to the bank. The angle with respect to the flow direction with which the boat should move to minimize the drift is (in $^{\circ}$)

Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

$A$ swimmer wants to cross a $200 \ m$ wide river which is flowing at a speed of $2 \ m/s$. The velocity of the swimmer with respect to the river is $1 \ m/s$. How far from the point directly opposite to the starting point does the swimmer reach the opposite bank (in $m$)?

$A$ river has a steady speed of $v$. $A$ man swims upstream for a distance of $d$ and swims back to the starting point in a total time $t$. The man can swim at a speed of $2v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same total distance of $2d$,then $\frac{t}{t_0}$ is