A particle $(A)$ moves due north at $3\,km / h$ another particle $(B)$ due west at $4\,km / h$. The relative velocity of $A$ with respect to $B$ is $\left(\tan 37^{\circ}=3 / 4\right)$
$5\,km / h , 37^{\circ}$ north of east
$5\,km / h , 37^{\circ}$ east of north
$5 \sqrt{2}\,km / h , 53^{\circ}$ east of north
$5 \sqrt{2}\,km / h , 53^{\circ}$ north of east
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 swimmer crosses a river of width $d$ flowing at velocity $v$. While swimming, he heads himself always at an angle of $120^{\circ}$ with the river flow and on reaching the other end he finds a drift of $d / 2$ in the direction of flow of river. The speed of the swimmer with respect to the river is
Rain is falling vertically with a speed of $30\,ms^{-1}$ . A woman rides a bicycle with a speed of $12\,ms^{-1}$ in east to west direction. She should hold her umbrella
A river is flowing from east to west at a speed of $5\, m/min$ A man on south bank of river, capable of swimming $10\,m/min$ in still water, wants to swim across the river in shortest time. He should swim