Question

Suppose that two objects A and B are moving with velocities ${\overrightarrow{v}}_{A}and{\overrightarrow{v}}_{B}$ (each with respect ot some common frame of reference). Let ${\overrightarrow{v}}_{AB}$represent the velocity of A with respect to B. Then

• A. ${\overrightarrow{v}}_{AB} + {\overrightarrow{v}}_{BA} = 0$
• B. ${\overrightarrow{v}}_{AB} - {\overrightarrow{v}}_{BA} = 0$
• C. ${\overrightarrow{v}}_{AB} = {\overrightarrow{v}}_{A} + {\overrightarrow{v}}_{B}$
• D. $|{\overrightarrow{v}}_{AB}| \neq |{\overrightarrow{v}}_{BA}|$

Answer 1

Answer: (A)

${\overrightarrow{v}}_{AB} + {\overrightarrow{v}}_{BA} = 0$

Answer 2

Velocity of object A relative to that of B is

${\overset{\rightarrow}{v}}_{AB} = {\overset{\rightarrow}{v}}_{B} - {\overset{\rightarrow}{v}}_{A}$

$\therefore{\overset{\rightarrow}{v}}_{AB} = - {\overset{\rightarrow}{v}}_{BA}$

And $\left| {\overset{\rightarrow}{v}}_{AB} \right| = \left| {\overset{\rightarrow}{v}}_{BA} \right|$