Question
Prove that $\vec{\text{v}}_\text{AB}=\vec{\text{v}}_\text{A}-\vec{\text{v}}_\text{B},$ where symbols have their usual meaning.
✓
Answer
Consider two bodies A and B moving with velocities VA and vg. Let x,; and xz; be their initial positions. Their position after time t is given by,
x1f = x1i + vAt
x2f = x2i + vBt
Subtacting,
(x1f - x2f) = (x1i - x2i) + t(vA - vB)
(x1f - x2f) - (x1i - x2i) = t(vA - vB)
The change in separation in time 't' is t(vA - vB).
(vA - vB) is called relative velocity of A with respect to B. It is nothig but the change in separation per unit time.
x1f = x1i + vAt
x2f = x2i + vBt
Subtacting,
(x1f - x2f) = (x1i - x2i) + t(vA - vB)
(x1f - x2f) - (x1i - x2i) = t(vA - vB)
The change in separation in time 't' is t(vA - vB).
(vA - vB) is called relative velocity of A with respect to B. It is nothig but the change in separation per unit time.
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