Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100 \text{ km/h}$ and $80 \text{ km/h}$, respectively, such that car $A$ is moving ahead of car $B$. $A$ person in car $B$ throws a stone with a speed $v$ so that it hits car $A$ with a speed of $5 \text{ m/s}$. The value of $v$ is . . . . . . $\text{km/h}$.

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

$A$ 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 $^{\circ}$)

$A$ 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)?

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 $\,s$)

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 (in $m\; s^{-1}$) of a monkey running on the roof of the train $A$ against its motion (with a velocity of $18\; km\; h^{-1}$ with respect to the train $A$) as observed by a man standing on the ground?