Objects A and B are at the origin. If object A moves to #(5 ,-1 )# and object B moves to #(-8 ,1 )# 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
Apr 26, 2016

Answer:

Treating the positive X-axis as North,
#color(white)("XXX")"approximately "4.38 m/(sec)" at "8.75^@ N" of "W#

Explanation:

The distance between points A and B has increased from #0# meters to
#color(white)("XXX")sqrt((5-(-8))^2+(1-(-1))^2)=sqrt(173)~~13.15# meters
for an average speed of
#color(white)("XXX")(sqrt(173) m)/(3 sec) ~~4.38 (m)/(sec)#

Relative to A, B has moved #13# meters East and #2# meters North.
If #theta# is the angle North of due East for B's movement relative to A then
#color(white)("XXX")tan(theta)=2/13#

#color(white)("XXX")rArr theta = arctan(2/13)~~8.75^@#

(Remember that velocity must always include a direction as well as a speed).