$A$ 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?

Particle $A$ (which was located at the origin at time $t=0$) is moving along the $x$-axis with a constant speed of $1 \,m/s$. The location of particle $B$, which is moving along the $y$-axis, is given by $y=ct^2$, where $c=1 \,m/s^2$. Find the speed of particle $A$ relative to particle $B$ at $t=1 \,s$.

$A$ shell is fired at a speed of $200\ m/s$ at an angle of $37^o$ above the horizontal from the top of a tower $80\ m$ high. At the same instant,another shell is fired from a jeep travelling away from the tower at a speed of $10\ m/s$ as shown. The velocity of this shell relative to the jeep is $250\ m/s$ at an angle of $53^o$ with the horizontal. Find the time (in $sec$) taken by the two shells to come closest.

$A$ moves with $65 \, km/h$ while $B$ is moving in the same direction as $A$ with $80 \, km/h$. The relative velocity of $B$ with respect to $A$ is ......... $km/h$.

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of the ground in $m \; s^{-1}$ with respect to train $B$?

$A$ stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of $12 \ km/h$,he observes that the rain is falling at an angle of $60^{\circ}$ with the vertical. The actual velocity of the rain is: