Question

Suppose you are riding a bike with a speed of $10m{s}^{-1}$ 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 $15m{s}^{-1}$, find the relative velocity between two reference frames A and B.

Answer 1

Taking east direction as positive (positive east)
$\overrightarrow{v_{you}}$ = 10 m/s
$\overrightarrow{v_{A,B}}$ = $\overrightarrow{v_{A,you}}$ + $\overrightarrow{v_{you,B}}$ ...(i)
$\overrightarrow{v_{you}}$ = $\overrightarrow{v_{you,A}}$ + $\overrightarrow{v_A}$ ...(ii)
As the direction of $\overrightarrow{v_{you,A}}$ and is both toward east. Hence, your direction should be toward east.
$\overrightarrow{v_{you,B}}$ = $\overrightarrow{v_{you}}$ - $\overrightarrow{v_B}$ ...(iii)
As B is moving toward west and you are moving towards east Hence, your direction w.r.t B should be toward east.
$\overrightarrow{v_{you,B}}$ = 15 m/s
Now from (i),$\overrightarrow{v_{A,B}}$ = -10 + 15 = 5 m/s
Hence, velocity of A w.r.t B will be 5 m/s toward east