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

$A$ man can swim with velocity $v$ relative to water. He has to cross a river of width $d$ flowing with a velocity $u$ $(u > v)$. The distance through which he is carried downstream by the river is $x$. Which of the following statements is correct?

$A$ river of width $200 \ m$ is flowing from west to east with a speed of $18 \ km/h$. $A$ boat,moving with a speed of $36 \ km/h$ in still water,is made to travel one round trip (bank to bank of the river). The minimum time taken by the boat for this journey and the displacement along the river bank are . . . . . . and . . . . . . respectively.

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 $^\circ$)?

$A$ swimmer swims in still water at a speed of $5 \text{ km/hr}$. He enters a $200 \text{ m}$ wide river,having a river flow speed of $4 \text{ km/hr}$,at point $A$ and proceeds to swim at an angle of $127^{\circ}$ $(\sin 37^{\circ} = 0.6)$ with the river flow direction. Another point $B$ is located directly across $A$ on the other side. The swimmer lands on the other bank at a point $C$,from which he walks the distance $CB$ with a speed of $3 \text{ km/hr}$. The total time in which he reaches from $A$ to $B$ is .......... $\text{minutes}$.

$A$ boy standing on the footpath tosses a ball straight up and catches it. The driver of a car passing by,moving with uniform velocity,sees this. The trajectory of the ball as seen by the driver will be: