There are two particles $P$ and $Q$ separated by a distance of $10 \ km$ and moving with velocities of $10 \ kmph$ as shown in the figure. The time elapsed before they reach their minimum separation is.........$hr$.

Explain this common observation clearly: If you look out of the window of a fast-moving train,the nearby trees,houses,etc.,seem to move rapidly in a direction opposite to the train's motion,but the distant objects (hilltops,the Moon,the stars,etc.) seem to be stationary. (In fact,since you are aware that you are moving,these distant objects seem to move with you).

$A$ man running at a speed of $5 \text{ km/h}$ finds that the rain falls vertically. When he stops running,he finds that the rain is falling at an angle of $60^{\circ}$ with the horizontal. The velocity of rain with respect to the running man is

$A$ man crosses a $320 \ m$ wide river perpendicular to the current in $4 \ minutes$. If in still water he can swim with a speed $5/3$ times that of the current,then the speed of the current,in $m/min$ is

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

It takes $1$ minute for a passenger standing on an escalator to reach the top. If the escalator does not move,it takes him $3$ minutes to walk up. How many seconds will it take for the passenger to arrive at the top if he walks up the moving escalator?