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

$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

$A$ person walks up a stalled escalator in $90 \, s$. When just standing on the same moving escalator,he is carried in $60 \, s$. The time it would take him to walk up the moving escalator will be $....... \, s$.

The stream of a river is flowing with a speed of $2\,km/h$. $A$ swimmer can swim at a speed of $4\,km/h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight (in $^\circ$)?

$A$ bird is flying to and fro between two cars moving towards each other on a straight road. One car has a speed of $18 \,km/h$ while the other has a speed of $27 \,km/h$. The bird starts moving from the first car towards the second car with a speed of $36 \,km/h$ when the two cars are separated by $36 \,km$. What is the total distance covered by the bird?

Car $A$ is moving to the East with a speed of $30 \text{ km/h}$,and car $B$ is moving to the North with the same speed. What is the velocity of car $B$ as measured from car $A$?