Objects A and B are at the origin. If object A moves to #(-6 ,7 )# and object B moves to #(-6 ,-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.

3 Answers
Apr 29, 2016

Answer:

#8/3ms^-1#

Explanation:

Relative velocity is a vector quantity. Lets check component wise:

  • x-component:
    Both the bodies have moved to the same vertical line, namely #x= -6# line. Hence their x-components of the velocities are same.

  • y-component:
    The distance between their final positions is: #(7-(-1)) = 8" m"#
    Hence the relative velocity along y-axis is: #8/3 ms^-1#

Hence the relative velocity is #8/3 ms^-1# along y-axis.

Apr 29, 2016

Answer:

#v_A=2,67 " m/s"#

Explanation:

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#"displacement=8 meters"#

#v_A=("displacement")/("time")#

#v_A=8/3#

#v_A=2,67 " m/s"#

Apr 29, 2016

In 3s displacement of A from (0.0) to (-6,7) #=vecd_A=(-6hati+7hatj)m#
Velocity of A , #vecV_A=vecd_A/3=1/3(-6hati+7hatj)m/s#

In 3s displacement of B from (0.0) to (-6,-1) #=vecd_B=(-6hati-hatj)m#
Velocity of B, #vecV_B=vecd_B/3=1/3(-6hati-hatj)m/s#
The relative velocity of object B from the perspective of object A
is #vecV_B-vecV_A=1/3(-6hati-hatj+6hati-7hatj)=-8/3hatjm/s#
So magnitude of relative velocity is #8/3m/s# and it is directed towards negative direction of y-axis i.e. #270^o# with positive direction of X-axis