$A$ swimmer can swim in still water with $5 \,m/s$. If a river is flowing with $4 \,m/s$, then find the time to cross the river of width $300 \,m$ if he has to reach the exactly opposite point.

$A$ man can swim with a speed of $4.0 \; km/h$ in still water. How long does he take to cross a river $1.0 \; km$ wide if the river flows steadily at $3.0 \; km/h$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

$A$ particle $(A)$ moves due north at $3\,km/h$ and another particle $(B)$ moves due west at $4\,km/h$. The relative velocity of $A$ with respect to $B$ is $(\tan 37^{\circ} = 3/4)$.

$A$ man is crossing a river flowing with a velocity of $5 \ m/s$. He reaches a point directly across at a distance of $60 \ m$ in $5 \ s$. His velocity in still water should be: (in $m/s$)

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days,if she remains stationary on the moving escalator,then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

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 . . . . . . $\text{km/h}$.