Relative Velocity MCQ - Practice Questions with Answers

• Relative change in position of one object with respect to another object.

• Formula-

           Relative velocity of object A with respect to object B.

                                          $\vec{V}_{A B}=\vec{V}_A-\vec{V}_B$

• Case of Relative Velocity

1. When A and B are moving along a straight line in the same direction.

$$
\begin{aligned}
& \overrightarrow{V_A}=\text { Velocity of object } \mathrm{A} \text {. } \\
& \overrightarrow{V_B}=\text { Velocity of object } \mathrm{B} .
\end{aligned}
$$

Then, the relative velocity of $A$ w.r. $B$ is

$$
\begin{gathered}
\vec{V}_{A B}=\vec{V}_A-\vec{V}_B \\
\vec{V}_{A B}, \vec{V}_A, \vec{V}_B \text { all are in the same direction. }\left(\mid f \vec{V}_A>\vec{V}_{B)}\right.
\end{gathered}
$$

           And Relative velocity of B w.r.t A is

 $\begin{aligned} \vec{V}_{B A} & =\vec{V}_B-\vec{V}_A \\ \& \vec{V}_{A B} & =-\vec{V}_{B A}\end{aligned}$

2. When A & B are moving along with straight line in the opposite direction.

          Relative velocity of A with respect to B is.

$\begin{aligned} & \vec{V}_{A B}=\vec{V}_A-\left(-\vec{V}_B\right) \\ & \vec{V}_{A B}=\vec{V}_A+\left(\vec{V}_B\right)\end{aligned}$

       3. Relative Velocity when bodies moving at an angle $\theta$ to each other

• Relative velocity of a body, A with respected body B 

$$
\begin{aligned}
V_{A B} & =\sqrt{V_A^2+V_B^2+2 V_A V_B \cos (180-\theta)} \\
& =\sqrt{V_A^2+V_B^2-2 V_A V_B \cos (\theta)}
\end{aligned}
$$

$$
\begin{aligned}
V_A & =\text { velocity of } A \\
V_B & =\text { velocity of } B
\end{aligned}
$$

Where,

$$
\Theta=\text { angle between } A \text { and } B
$$
 

• If $\overrightarrow{V_{A B}}$ makes an angle $\beta$ with the direction of $\overrightarrow{V_A}$, then

  $$
  \begin{aligned}
  & \tan \beta=\frac{V_B \sin (180-\Theta)}{V_A+V_B \cos (180-\Theta)} \\
  & =\frac{V_B \cdot \sin \Theta}{V_A-V_B \cos \Theta}
  \end{aligned}
  $$
   

• If two bodies are moving at right angles to each other.

           Relative Velocity of A with respect to B is

                            $V_{A B}=\sqrt{V_A^2+V_B^2}$