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
Alan P.
Sep 26, 2016

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^@
enter image source here

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