Question

Objects A and B are at the origin. If object A moves to `(-7 ,5 )` and object B moves to `(-5 ,-2 )` over `2 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

`vecv_{Ag} =(-7/2, 5/2);\qquad vecv_{Bg} = (-5/2, -1);`

`vecv_{BA} = vecv_{Bg} + vecv_{gA} = vecv_{Bg} - vecv_{Ag} = (1, 7/2);`

Explanation:

Velocity of A relative to ground:
`vecv_{Ag} = (\Deltavecr_A)/(\Deltat) = ((-7,5)-(0,0))/2=(-7/2, 5/2);`

Velocity of B relative to ground:
`vecv_{Bg} = (\Deltavecr_B)/(\Deltat) = ((-5-2)- (0,0))/2=(-5/2, -1);`

Velocity of B relative to A:
`vecv_{BA} = vecv_{Bg} + vecv_{gA} = vecv_{Bg} - vecv_{Ag};`

`vecv_{BA} = (-5/2, -1)-(-7/2,5/2) = (1, 7/2);`