Objects A and B are at the origin. If object A moves to #(-5 ,2 )# and object B moves to #(-1 ,-8 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?

1 Answer
Mar 24, 2017

Answer:

Relative velocity (approximately): #color(green)(2.7)# units/sec at an angle of #color(green)(-68.2^@)#

Explanation:

Here is a graph of the resultant positions:
enter image source here

The relative displacement of #B# with respect to #A# is
#color(white)("XXX")4 " units horizontally"# and
#color(white)("XXX")-10 " units vertically"#.

The angle of displacement (to #B# relative to #A#) is therefore
#color(white)("XXX")arctan((-10)/4)~~-1.19028995" (radians)" ~~-68.19859051^@#
(calculator used for this)

The distance from #A# to #B# (using the Pythagorean Theorem) is
#color(white)("XXX")sqrt(4^2+(-10)^2)=sqrt(116)=2sqrt(29)" units"#

Since this distance was covered over a period of #4# sec.
the average speed must be #(2sqrt(29))/4 " units/sec" ~~2.69258..." units/sec."#

velocity is a combination of speed and angle.