$A$ 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 $\,s$)

Wind is blowing in the north direction at a speed of $2 \, m/s$,which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?

$A$ 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 ......... $km/hr$.

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ man cycling with a speed of $20 \,km/h$ from $A$ to $B$ notices that a bus travelling in the direction of his motion goes past him every $18 \,min$ and every $6 \,min$ he notices a bus travelling in the opposite direction go past him. Assuming that the buses travel with a constant speed,find $T$ and the constant speed of the buses.

$A$ 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 $m/s$?

$A$ jet airplane travelling at the speed of $500 \; km \; h^{-1}$ ejects its products of combustion at the speed of $1500 \; km \; h^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?