Relative Motion
RELATIVE VELOCITY
1.If \(\vec v_A\) and \(\vec V_B\) are the velocities of A and B then relative velocity of A with respect to B is \(\vec V_A -\vec V_B\) and relative velocity of B with respect to A is \(\vec V_B-\vec V_A\)
If \(\theta\) is the angle between \(\overrightarrow V_A\) and \(\overrightarrow V_B\)
|\(\overrightarrow V_A-\overrightarrow V_B\) |or |\(\overrightarrow V_B-\overrightarrow V_A\)|= \(
\sqrt {V_A ^2 + V_B ^2 - 2V_A V_B \cos \theta }
\)
If \(\theta=0^0\) i.e., \(\overrightarrow V_A\) || \(\overrightarrow V_B\)
|\(\overrightarrow V_A-\overrightarrow V_B\)|= \(\overrightarrow V_A\)- \(\overrightarrow V_B\) and | \(\overrightarrow V_B-\overrightarrow V_A\)|= VB+VA
If \(\theta=180^0\) i.e., \(\overrightarrow V_A\) is parallel to –\(\overrightarrow V_B\) ( \(\overrightarrow V_A\) is antiparallel to \(\overrightarrow V_B\) )
|\(\overrightarrow V_A-\overrightarrow V_B\)|= \(\overrightarrow V_A\)+\(\overrightarrow V_B\) and |\(\overrightarrow V_B-\overrightarrow V_A\)|= \(V_B\)+\(V_A\)
If \(\theta=90^0\) i.e., \(
V_A \bot V_B
\)
|\(
\overrightarrow V _A - \overrightarrow V _B
\)| or |\(
\overrightarrow V _B - \overrightarrow V _A
\)|=\(
\sqrt {V_A ^2 + V_B ^2 }
\)