Question

If \( V_A \) and \( V_B \) are velocities of A and B respectively and their directions are normal to each other, the relative velocity of A with respect to B is

• A. \( V_A + V_B \)
• B. \( V_A - V_B \)
• C. \( \sqrt{V_A^2 + V_B^2} \)
• D. \( \sqrt{V_A^2 - V_B^2} \)

Hint:

When velocities are perpendicular to each other, the relative velocity is found using the Pythagorean theorem.

Answer 1

The Correct Option is C

Step 1: Use the formula for relative velocity.
When two velocities are perpendicular (normal to each other), the magnitude of the relative velocity \( V_{AB} \) of A with respect to B is given by: \[ V_{AB} = \sqrt{V_A^2 + V_B^2}. \]
Step 2: Conclusion.
Thus, the relative velocity of A with respect to B is \( \sqrt{V_A^2 + V_B^2} \), corresponding to option (C).