$A$ person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5\, m/s$ at an angle of $120^\circ$ with the direction of flow of water. The speed of water in the stream is..........$m/s$.

$A$ man swimming downstream overtakes a float at a point $M$. After travelling a distance $D$,he turns back and passes the float at a distance of $D/2$ from the point $M$. The ratio of the speed of the swimmer with respect to still water $(v_s)$ to the speed of the river $(v_r)$ is:

Particle $A$ moves along the $X$-axis with a uniform velocity of magnitude $10 \ m/s$. Particle $B$ moves with a uniform velocity of $20 \ m/s$ along a direction making an angle of $60^{\circ}$ with the positive direction of the $X$-axis as shown in the figure. The relative velocity of $B$ with respect to $A$ is

$A$ bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane,the trajectory of the bomb is a:

$A$ bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of $54 \text{ kmh}^{-1}$ while the other has a speed of $36 \text{ kmh}^{-1}$. The bird starts moving from the first car towards the other and is moving with a speed of $36 \text{ kmh}^{-1}$ when the two cars are separated by $36 \text{ km}$. The total distance covered by the bird before the cars meet each other is: (in $\text{ m}$)

$A$ river is flowing from east to west at a speed of $5\, m/min$. $A$ man on the south bank of the river,capable of swimming $10\, m/min$ in still water,wants to swim across the river in the shortest time. He should swim: