The velocities of $A$ and $B$ are $\vec{v}_A=2 \hat{i}+4 \hat{j}$ and $\vec{v}_B=3 \hat{i}-7 \hat{j}$ Velocity of $B$ as observed by $A$ is ..........

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

A bus appears to go with a speed of $25 \,km / hr$ to a car driver, driving at the rate $7 \,km / hr$ northwards. If the bus actually travels in east direction, its speed is ......... $km / h$

A river is flowing from west to east at a speed of $8\,m$ per 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 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

A man goes $10\,km$ downstream in $2\,hrs$ and $30\,km$ upstream in $10\,hrs$ . How much time will be take to swim $40\,km$ in still water........$hrs$