Question

Two particles are moving with the velocities $v_1$ and $v_2$. The relative velocity between the particles will be maximum when the angle between their velocities will be

• A. $0$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B

$\pi$

Relative velocity:

1. Relative velocity can be defined as the velocity of an object with respect to the velocity of another object.
2. When two objects move in the same direction, the relative velocity between them gets reduced.
3. When the objects move in the opposite direction, the relative velocity between them gets increased.

Step 1: Vector representation of relative velocity

The vector representation of the relative velocity can be expressed as follows:

${\mathrm{V}}_{\mathrm{AB}}={\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_{\mathrm{B}}$

Here, ${\mathrm{V}}_{\mathrm{AB}}$ is the relative velocity of $\mathrm{A}$ with respect to $\mathrm{B}$, ${\mathrm{V}}_{\mathrm{A}}$ is the velocity of $\mathrm{A}$, and ${\mathrm{V}}_{\mathrm{B}}$ is the velocity of $\mathrm{B}$.

Step 2: Diagram of the condition for the maximum relative velocity

The relative velocity will be maximum if the particles move in the opposite direction.

$$\begin{gathered} {\mathrm{V}}_{\mathrm{AB}}={\mathrm{V}}_{\mathrm{A}}-\left(-{\mathrm{V}}_{\mathrm{B}}\right) \\ {\mathrm{V}}_{\mathrm{AB}}={\mathrm{V}}_{\mathrm{A}}+{\mathrm{V}}_{\mathrm{B}} \end{gathered}$$

Hence, the relative velocity between the particles will be maximum when the particles will move in the opposite direction, or at an angle$\pi$.