Question

A jet airplane travelling from east to west at a speed of $500\, km \, h ^{-1}$ ejected out gases of combustion at a speed of $1500\, km\, h ^{-1}$ with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?

• A. $1000\, km\, h ^{-1}$ in the direction west to east
• B. $1000\, km\, h ^{-1}$ in the direction east to west
• C. $2000 \, km\, h ^{-1}$ in the direction west to east
• D. $2000\, km \, h ^{-1}$ in the direction east to west

Answer 1

Answer: (B)

$ \vec{v}_{A}=-500 \hat{i} $
and $ \vec{v}_{G A}=1500 \hat{i} $
$\Rightarrow \vec{v}_{G A}+\vec{v}_{A}=\vec{v}_{G A S} $
$ \Rightarrow \vec{v}_{G A S}=1500 \hat{i}-500 \hat{i}=1000 \hat{i}$