Objects A and B are at the origin. If object A moves to #(4 ,-2 )# and object B moves to #(5 ,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
Sep 26, 2016

Answer:

Velocity: #0.7603# m/sec at #80.54^@# (measuring counter clockwise from the X-axis)

Explanation:

Note that it doesn't matter that #A# and #B# started at the origin; it only matters that they started at the same place.

The initial distance between #A# and #B# is #0# (meters)
The distance between #A# and #B# after #8# seconds is
#color(white)("XXX")sqrt((5-4)^2+(4-(-2))^2)=sqrt(37)# (meters)

Since this is the change in position relative to each other
the relative speed of #B# from #A#'s perspective is
#color(white)("XXX")(sqrt(37) "meters")/(8 "seconds") ~~0.7603453 "m/sec"#

The tan of the angle (relative to the horizontal/X-axis) is #6/1# (see diagram below).

Therefore the angular component of the velocity is
#color(white)("XXX")"arctan"(6) ~~80.53768^@#
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