$A$ 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 $^{\circ}$)

$A$ man can swim with a speed of $4 \ km/h$ in still water. How long does he take to cross a river $1 \ km$ wide, if the river flows steadily at $3 \ km/h$ and he makes his strokes normal to the river current (in $min$)?

The velocities of $A$ and $B$ are $\vec{v}_A = 2 \hat{i} + 4 \hat{j}$ and $\vec{v}_B = 3 \hat{i} - 7 \hat{j}$. The velocity of $B$ as observed by $A$ is:

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \ km/hr$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be ......... $km/hr$.

Two particles $A$ and $B$ are moving in a horizontal plane as shown in the figure at $t = 0$. The time after which $A$ will catch $B$ is.......$s$.

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 $.5$)