Question

Suppose you are riding a bike with a speed of $20m/s$ due east relative to a person 𝐴 who is walking on the ground towards east. If your friend 𝐵 walking on the ground due west measures your speed as $30m/s$, find the relative velocity between two reference frames 𝐴 and 𝐵.

• A. Velocity of A w.r.t. B is $10m/s$ towards east
• B. Velocity of A w.r.t. B is $10m/s$ towards west
• C. Velocity of A w.r.t. B is $5m/s$ towards west
• D. Velocity of A w.r.t. B is $5m/s$ towards east

Answer 1

The correct option is A Velocity of A w.r.t. B is $10m/s$ towards east

Given:
Speed of person A towards east with respect to you $\left({\overrightarrow{v}}_{A,you}\right)=-20m/s$
Speed of you with respect to person 𝐵 towards west $\left({\overrightarrow{v}}_{you,B}\right)=30m/s$
Therefore, velocity of 𝐴 with respect to 𝐵 is given by,
${\overrightarrow{v}}_{AB}={\overrightarrow{v}}_{A,you}+{\overrightarrow{v}}_{you,B}$
${\overrightarrow{v}}_{AB}=-{\overrightarrow{v}}_{you,A}+{\overrightarrow{v}}_{you,B}$
By putting the values in the given equation, we get,
${\overrightarrow{v}}_{AB}=(-20)+30$
${\overrightarrow{v}}_{AB}=10m/s$east
Final Answer: (C)