$A$ 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 $m$)?

$A$ police jeep is chasing a thief's jeep. The police jeep is moving with a velocity of $45 \, km/h$ and the thief's jeep is moving with a velocity of $153 \, km/h$. The police fire a bullet with a muzzle velocity of $180 \, m/s$. What is the velocity with which the bullet strikes the thief's car in $m/s$?

$A$ 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 figure shows two ships moving in the $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

Two particles $A$ and $B$ move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment,their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles $A$ and $B$ to collide is:

$A$ swimmer can swim in still water with speed $v$ and the river is flowing with velocity $v/2$. To cross the river in the shortest distance,the swimmer should swim at an angle $\theta$ with the upstream. What is the ratio of the time taken to swim across in the shortest time to the time taken to swim across the shortest distance?