$A$ train is moving slowly on a straight track with a constant speed of $2 \,ms^{-1}$. $A$ passenger in that train starts walking at a steady speed of $2 \,ms^{-1}$ to the back of the train in the opposite direction of the motion of the train. To an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be:

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

$A$ person is swimming with a speed of $10\, m/s$ at an angle of $120^{\circ}$ with the flow of the river and reaches a point directly opposite on the other side. If the speed of the river flow is $x\, m/s$,find the value of $x$ to the nearest integer.

$A$ boat is moving with a velocity of $3\hat i + 4\hat j$ in a river,and the water is moving with a velocity of $-3\hat i - 4\hat j$ with respect to the ground. The relative velocity of the boat with respect to the water is:

$A$ river is flowing due east with a speed $3\, ms^{-1}$. $A$ swimmer can swim in still water at a speed of $4\, ms^{-1}$ (figure).
$(a)$ If the swimmer starts swimming due north,what will be his resultant velocity (magnitude and direction)?
$(b)$ If he wants to start from point $A$ on the south bank and reach the opposite point $B$ on the north bank,
$(i)$ In which direction should he swim?
$(ii)$ What will be his resultant speed?
$(c)$ From the two different cases as mentioned in $(a)$ and $(b)$ above,in which case will he reach the opposite bank in a shorter time?

Out of the two cars $A$ and $B$,car $A$ is moving towards the east with a velocity of $10 \, m/s$,whereas car $B$ is moving towards the north with a velocity of $20 \, m/s$. The velocity of $A$ with respect to $B$ is ......... $m/s$ (nearly).