Question

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.

Answer 1

`\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)`