$A$ butterfly is flying with a velocity $4 \sqrt{2} \, m/s$ in the North-East direction. The wind is blowing at $1 \, m/s$ from North to South. The resultant displacement of the butterfly in $3 \, s$ is $.... \, m$.

$A$ 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

Two cars $A$ and $B$ are moving with a velocity of $30 \ km/h$ in the same direction. They are separated by $10 \ km$. The speed of another car $C$ moving in the opposite direction,if it meets these two cars at an interval of $8 \ minutes$,is: (in $km/h$)

$A$ 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 $m/s$?

Two trains, each $30 \,m$ long, are travelling in opposite directions with velocities $5 \,m/s$ and $10 \,m/s$. They will cross each other after: (in $\,s$)

Two particles are moving along two long straight lines,in the same plane,with the same speed $= 20 \, cm/s$. The angle between the two lines is $60^{\circ}$,and their intersection point is $O$. At a certain moment,the two particles are located at distances $3 \, m$ and $4 \, m$ from $O$,and are moving towards $O$. Subsequently,the shortest distance between them will be