First slide

Relative motion in 2 dimension

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?

Easy

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

Solution

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

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