When a train is at rest,rain drops fall vertically. When it moves along east with a velocity equal to that of rain,the rain will appear to fall,for a passenger in the train

$A$ $2\,m$ wide truck is moving with a uniform speed $v_0=8\,m/s$ along a straight horizontal road. $A$ pedestrian starts to cross the road with a uniform speed $v$ when the truck is $4\,m$ away from him. The minimum value of $v$ so that he can cross the road safely is $...........\,m/s$.

$A$ river has a steady speed of $v$. $A$ man swims upstream for a distance of $d$ and swims back to the starting point in a total time $t$. The man can swim at a speed of $2v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same total distance of $2d$, then $\frac{t}{t_0}$ is

Two girls are standing at the ends $A$ and $B$ of a ground where $AB = b$. The girl at $B$ starts running in a direction perpendicular to $AB$ with velocity $V_1$. The girl at $A$ starts running simultaneously with velocity $V_2$ and meets the other girl in the shortest possible time $t$. The value of $t$ is:

$A$ man can swim with a speed of $4.0 \; km/h$ in still water. How long does he take to cross a river $1.0 \; km$ wide if the river flows steadily at $3.0 \; km/h$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

If the velocities of particles $A$ and $B$ with respect to the ground are ${\overrightarrow v _A}$ and ${\overrightarrow v _B}$ respectively,then:
$(a)$ Write the formula for the velocity of $A$ with respect to $B$.
$(b)$ Write the formula for the velocity of $B$ with respect to $A$.
$(c)$ Is the relation ${\overrightarrow v _{AB}} = -{\overrightarrow v _{BA}}$ correct?