$A$ boat takes $2 \, h$ to travel $8 \, km$ and back in still water. If the velocity of water is $4 \, km/h$,the time taken for going upstream $8 \, km$ and coming back is:

$A$ 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?

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ man cycling with a speed of $20 \,km/h$ from $A$ to $B$ notices that a bus travelling in the direction of his motion goes past him every $18 \,min$ and every $6 \,min$ he notices a bus travelling in the opposite direction go past him. Assuming that the buses travel with a constant speed,find $T$ and the constant speed of the buses.

$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

$A$ butterfly is flying with a velocity $4 \sqrt{2} \, m/s$ in the North-East direction. The wind is blowing at $1 \, m/s$ from North to South. The resultant displacement of the butterfly in $3 \, s$ is $.... \, m$.

$A$ 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 $m$)?