Two particles $A$ and $B$ are moving in a horizontal plane as shown in the figure at $t = 0$. The time after which $A$ will catch $B$ is.......$s$.

When is the relative velocity of two cars moving with unequal velocities less than the individual velocity of either car?

Two boys are standing at points $A$ and $B$ on the ground,where distance $AB = x$. The boy at $B$ starts running perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and meets the other boy in time $t$. The value of $t$ is:

Two particles $A$ and $B$ move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment,their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles $A$ and $B$ to collide is:

Rain is falling vertically with a speed of $35 \; m s^{-1}$. $A$ woman rides a bicycle with a speed of $12 \; m s^{-1}$ in the east to west direction. What is the direction in which she should hold her umbrella?

$A$ 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