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
Alan P.
Apr 26, 2016

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).

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