Two trains,each $50 \, m$ long,are travelling in opposite directions with velocities $10 \, m/s$ and $15 \, m/s$. The time taken for them to cross each other is:

$A$ steam boat goes across a lake and comes back: $(i)$ on a quiet day when the water is still and $(ii)$ on a rough day when there is a uniform current so as to help the journey onward and to impede the journey back. If the speed of the launch,on both days,was same,the time required for the complete journey on the rough day as compared to that on the quiet day,will be

On a long horizontally moving belt,a child runs to and fro with a speed $9 \, km \, h^{-1}$ (with respect to the belt) between his father and mother located $50 \, m$ apart on the moving belt. The belt moves with a speed of $4 \, km \, h^{-1}$. For an observer on a stationary platform,the speed of the child running in the direction of motion of the belt is ..... $km \, h^{-1}$.

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:

$A$ train of $150 \,m$ length is going towards north direction at a speed of $10 \,ms^{-1}$. $A$ parrot flies at the speed of $5 \,ms^{-1}$ towards south direction parallel to the railway track. The time for which the parrot flies alongside the train is (in $\,s$)

The width of the river is $1 \; km$. The velocity of the boat is $5 \; km/hr$. The boat covers the width of the river along the shortest possible path in $15 \; min$. The velocity of the river stream is: