Objects A and B are at the origin. If object A moves to #(3 ,6 )# and object B moves to #(6 ,-5 )# over #1 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
Jul 30, 2017

Answer:

#vec v_(B w.r.t A)=3 hat i - 11 hat j#

Explanation:

#vec r_i#= initial displacement vector
#vec r_j#=final displacement vector
#vec r_A#=Displacement vector of A
#vec r_B#=Displacement vector of B
w.r.t=with respect to

#vec r_i=vec 0#
#vec r_f=3hati + 6hatj#
#vec r_A= vec r_f - vec r_i#
#vec r_A=3hati + 6hatj#

#vec r_i=vec 0#
#vec r_f=6hati - 5hatj#
#vec r_B= vec r_f - vec r_i#
#vec r_B=6hati - 5hatj#

#vec r_(B w.r.t A) = vec r_B - vec r_A#

#vec r_(B w.r.t A) = 3hati - 11hatj (m)#

#vec v_(B w.r.t A)=(vec r_(B w.r.t A))/t#

#vec v_(B w.r.t A)= (3hati - 11hatj (m))/(1s)#

#vec v_(B w.r.t A)= 3hati - 11hatj (m*s^-1) #

#|vec v_(Bw.r.tA)| = sqrt(130) m*s^-1#