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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