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Question
Suppose that two objects A and B are moving with velocities `vec("V"_"A")` and `vec("V"_"B")` (each with respect to some common frame of reference). Let `vec("V"_"AB")` represents the velocity of A with respect to B then:
Options
`vec("V"_"AB") + vec("V"_"BA") = 0`
`vec("V"_"AB") - vec("V"_"BA") = 0`
`vec("V"_"AB") ≠ vec("V"_"A") + vec("V"_"B")`
`|vec("V"_"AB")| ≠ |vec("V"_"BA")|`
MCQ
Solution
`vec("V"_"AB") + vec("V"_"BA") = 0`
Explanation:
Velocity of object A relative to that of object B is
`vec("V"_"AB") = vec("V"_"A") - vec("V"_"B")`
Velocity of object B relative to that of A is
∴ `vec("V"_"BA") = vec("V"_"B") - vec("V"_"A")`
∴ `vec("V"_"BA") = vec(-"V"_"AB")` and `|vec("V"_"AB")| = |vec("V"_"BA")|`
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