Two cars $A$ and $B$ are moving with speeds $v_A = 120 \text{ km/h}$ and $v_B = 50 \text{ km/h}$ respectively in the directions as indicated by the arrows in the figure below. What is the relative speed of car $B$ with respect to car $A$ (in $\text{ km/h}$)?

$A$ train of $150 \ m$ length is going towards the north direction at a speed of $10 \ m/s$. $A$ parrot flies at a speed of $5 \ m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is........$s$.

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 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 $min$)?

$A$ river is flowing from $W$ to $E$ with a speed of $5 \, m/min$. $A$ man can swim in still water with a velocity of $10 \, m/min$. In which direction should the man swim to take the shortest possible path to reach the opposite bank (South)?

$A$ bird is flying to and fro between two cars moving towards each other on a straight road. One car has a speed of $18\,km/h$ while the other has a speed of $27\,km/h$. The bird starts moving from the first car towards the other with a speed of $36\,km/h$. If the two cars were initially separated by $36\,km$,what is the total distance covered by the bird?