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.

                                          ${\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A-{\overrightarrow{V}}_B$

• Case of Relative Velocity

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

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

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

$$\begin{array}{c}{\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A-{\overrightarrow{V}}_B\\ {\overrightarrow{V}}_{AB},{\overrightarrow{V}}_A,{\overrightarrow{V}}_B\text{ all are in the same direction. }(\mid f{\overrightarrow{V}}_A>{\overrightarrow{V}}_{B)}\end{array}$$

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

 $\begin{array}{rl}{\overrightarrow{V}}_{BA}& ={\overrightarrow{V}}_B-{\overrightarrow{V}}_A\\ \mathrm{\&}{\overrightarrow{V}}_{AB}& =-{\overrightarrow{V}}_{BA}\end{array}$

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

          Relative velocity of A with respect to B is.

$\begin{array}{rl}& {\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A-(-{\overrightarrow{V}}_B)\\ & {\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A+\left({\overrightarrow{V}}_B\right)\end{array}$

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

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

$$\begin{array}{rl}{V}_{AB}& =\sqrt{V_A^2+V_B^2+2V_A{V}_B\cos (180-\theta )}\\ & =\sqrt{V_A^2+V_B^2-2V_A{V}_B\cos (\theta )}\end{array}$$

$$\begin{array}{rl}{V}_A& =\text{ velocity of }A\\ V_B& =\text{ velocity of }B\end{array}$$

Where,

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

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

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

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

           Relative Velocity of A with respect to B is

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