Objects A and B are at the origin. If object A moves to #(3 ,1 )# and object B moves to #(2 ,4 )# over #8 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
Alan P.
Jul 8, 2016

(Using the positive Y-axis as North)
#1.118 m/s " at "47.16^@ W of N#

Explanation:

Distance after #8 s# between A and B
#color(white)("XXX")d=sqrt((3-2)^2+(1-4)^2)=sqrt(10)# (m)
Speed of B relative to A: #sqrt(10)/8 m/s ~~1.118 m/s#

If #theta# is the angle from A to B (relative to the Y-axis)
then #tan(theta)=(4-1)/(2-3)=-3#
#rArr theta~~137.16^@# (relative to the positive X-axis)
or
#color(white)("XXX")47.16^@# (relative to the Y-axis)

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