Objects A and B are at the origin. If object A moves to (-6 ,-5 ) and object B moves to (-1 ,4 ) over 3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

1 Answer
Cosmic Defect
Mar 1, 2016

\vec{v_{AB}} = (-6, -5)-(-1, 4)=(-5, -9)

Explanation:

Relative Velocities Rules:
[1] \vec{v_{AC}} = \vec{v_{AB}} + \vec{v_{BC}};
[2] \vec{v_{AB}} = - \vec{v_{BA}}

\vec{v_{AB}} - Velocity of A relative to B,\qquad \vec{v_{BC}} - Velocity of B relative to C,
\vec{v_{AC}} - Velocity of A relative to C,

Taking ground as the reference frame C

\vec{v_{AB}} - Velocity of A relative to B,
\vec{v_{Bg}} = (-1, 4) - Velocity of B relative to ground,
\vec{v_{Ag}} = (-6, -5) - Velocity of A relative to ground,

\vec{v_{Ag}} = \vec{v_{AB}}+\vec{v_{Bg}}
\vec{v_{AB}} = \vec{v_{Ag}} - \vec{v_{Bg}} = (-6, -5) - (-1, 4)=(-5,-9)

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