$A$ $120 \, m$ long train is moving towards west with a speed of $10 \, m/s$. $A$ bird flying towards east with a speed of $5 \, m/s$ crosses the train. The time taken by the bird to cross the train will be ........ $sec$.

$A$ boat covers a certain distance between two spots in a river taking $t_1$ hours going downstream and $t_2$ hours going upstream. What time will be taken by the boat to cover the same distance in still water?

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.......$s$.

The speed of a swimmer is $4\,km\,h^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of a river of width $1\,km$,he reaches a point $750\,m$ downstream on the opposite bank. The speed of the river water is $.........\,km\,h^{-1}$.

Ship $A$ is sailing towards north-east with velocity $\vec{v}_A = 30\hat{i} + 50\hat{j}\,\text{km/hr}$,where $\hat{i}$ points east and $\hat{j}$ points north. Ship $B$ is at a distance of $80\,\text{km}$ east and $150\,\text{km}$ north of Ship $A$ and is sailing towards west at $10\,\text{km/hr}$. After how many hours will Ship $A$ be at the minimum distance from Ship $B$?

$A$ police jeep is chasing a thief's jeep. The police jeep is moving with a velocity of $45 \, km/h$ and the thief's jeep is moving with a velocity of $153 \, km/h$. The police fire a bullet with a muzzle velocity of $180 \, m/s$. What is the velocity with which the bullet strikes the thief's car in $m/s$?