$A$ passenger sitting in a train $A$ moving at $90\,km/h$ observes another train $B$ moving in the opposite direction for $8\,s$. If the velocity of the train $B$ is $54\,km/h$,then the length of train $B$ is $..........\,m$.

$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with the same speed $v$. The actual velocity of $Y$ is $........$.

Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed $u$ along the track so that the relative velocities of the trains with respect to the wind are in the ratio of $1:2$,then the speed of each train must be

Ram moves in the east direction at a speed of $6 \, m/s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \, m/s$. The magnitude of their relative velocity is ........ $m/s$.

$A$ boy throws a ball in the air at $60^{\circ}$ to the horizontal,along a road with a speed of $10 \, m/s$. Another boy sitting in a passing car observes the ball. Sketch the motion of the ball as observed by the boy in the car,if the car has a speed of $18 \, km/h$. Give an explanation to support your diagram.

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \ km/hr$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be ......... $km/hr$.