Question

Suppose that two objects $A$ and $B$ are moving with velocities $\overrightarrow{ V _{ A }}$ and $\overrightarrow{ V _{ B }}$ (each with respect to some common frame of reference). Let $\overline{ V _{ AB }}$ represents 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. $\overrightarrow{ V }_{ AB } \neq \overrightarrow{ V }_{ A }+\overrightarrow{ V }_{ B }$
• D. $\left|\overrightarrow{ V }_{ AB }\right| \neq\left|\overrightarrow{ V }_{ BA }\right|$

Answer 1

Answer: (A)

Velocity of object A relative to that of object $B$ is
$\overrightarrow{ V }_{ AB }=\overrightarrow{ V }_{ A }-\overrightarrow{ V }_{ B }$
Velocity of object B relative to that of $A$ is
$\therefore \overrightarrow{ V }_{ BA }=\overrightarrow{ V }_{ B }-\overrightarrow{ V }_{ A }$
$\therefore \overrightarrow{ V }_{ BA }=-\overrightarrow{ V }_{ AB }$
and $\left|\overrightarrow{ V }_{ AB }\right|=\left|\overrightarrow{ V }_{ BA }\right|$