Objects A and B are at the origin. If object A moves to #(3 ,-2 )# and object B moves to #(2 ,9 )# over #5 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
Oct 10, 2016

Answer:

Relative velocity of #B# with respect to #A# is #2.21 " m/s"# at an angle of #95.2^@# (relative to the positve X-axis)

Explanation:

After moving #A# to #(3,-2)# and #B# to #(2,9)#
from #A#'s perspective #B# has moved #<-1,11>#
for a distance of #sqrt((-1)^2+11^2) = sqrt(122)#
Since this apparent motion takes place over #5# seconds
the apparent speed is #sqrt(122)/5 " m/s"~~2.21 " m/s"#

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The angle of this apparent motion, #theta# (relative to the positive X-axis) is such that #tan(theta)=11/(-1)#

#"arctan(-11/1) ~~1.66# (radians) #~~95.2^@#