Suppose that two objects A and B are moving with velocities V A and V B (each with respect to some common frame of reference). Let overline V AB represents the velocity of A with respect to B then:

Question

Suppose that two objects A and B are moving with velocities V A and V B (each with respect to some common frame of reference). Let overline V AB represents the velocity of A with respect to B then: (A)  V AB + V BA =0 (B)  V AB - V BA =0 (C)  V AB ≠ V A + V B  (D) | V AB | ≠| V BA |

Tardigrade Admin · Accepted Answer

Velocity of object A relative to that of object B is V AB = V A - V B Velocity of object B relative to that of A is ∴ V BA = V B - V A ∴ V BA =- V AB and | V AB |=| V BA |

Q. Suppose that two objects $A$ and $B$ are moving with velocities $V_{A}$ and $V_{B}$ (each with respect to some common frame of reference). Let $\overline{V_{A B}}$ represents the velocity of A with respect to B then:

$V_{A B} + V_{B A} = 0$

$V_{A B} - V_{B A} = 0$

$V_{A B} \neq = V_{A} + V_{B}$

$∣ ∣ V_{A B} ∣ ∣ \neq = ∣ ∣ V_{B A} ∣ ∣$

Velocity of object A relative to that of object $B$ is
$V_{A B} = V_{A} - V_{B}$
Velocity of object B relative to that of $A$ is
$∴ V_{B A} = V_{B} - V_{A}$
$∴ V_{B A} = - V_{A B}$
and $∣ ∣ V_{A B} ∣ ∣ = ∣ ∣ V_{B A} ∣ ∣$

Q. Suppose that two objects A and B are moving with velocities VA​​ and VB​​ (each with respect to some common frame of reference). Let VAB​​ represents the velocity of A with respect to B then:

VAB​+VBA​=0

VAB​−VBA​=0

VAB​=VA​+VB​

∣∣​VAB​∣∣​=∣∣​VBA​∣∣​