Objects A and B are at the origin. If object A moves to (-7 ,5 )(7,5) and object B moves to (-5 ,-2 )(5,2) over 2 s2s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

1 Answer
Dec 3, 2017

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);