Relative Motion

Key Questions

• What is the relative velocity equation?

  Answer:

  If an object A moves with velocity #vecv""_A# and object B with #vecv""_B#, Then velocity of A with respect to B (As observed by observer B) is,

  #vecv""_(AB)# = #vecv""_A - vecv""_B#.

  Explanation:

  As an example, let us consider linear motion for simplicity and assume that our observations in one dimension holds for two and three dimensions. (By using vector notation, this happily turns out to be the case.)

  Two cars A and B moving with velocities #v""_A# and #v""_B#.

  Velocity of A as observed by a person sitting in car B is then naturally,

  #v""_(AB) = v""_A - v""_B#

  if #v""_A# is greater than #v""_B#.

  The observer sees the car A going away (ahead) from it with speed #v""_(AB)#.

  If the opposite is the case, #v""_(AB)# is negative.

  The car B goes ahead of A with the speed #v""_(AB)#.

  Extending what we observed here to three dimensions is trivial.
  We just have to use vector notations for that. Other details remain unchanged.

  Aritra G. · 1 · Jul 26 2015
• What is relative motion?

  Relative motion is the velocity of one mass with respect to another, even though both may be moving with respect to an observer.

  An easy way to think about this is if you are standing next to a highway and two cars go past, one at 50 MPH and the other at 52 MPH. Even though the motion of both cars is fast compared to you, the driver of each car looks at the other and sees that the relative motion of the two cars is only 2 MPH. Keeping relative speeds low on our highways is an important key to highway safety!

  Chuck W. · · May 15 2014

• Why is acceleration inversely proportional to mass?
• Why is acceleration negative in a free fall?
• When is acceleration constant?
• Why is acceleration a vector quantity?
• What is the relative speed of particles in a liquid?
• What is the relative velocity equation?
• What is relative speed between two objects?
• How does acceleration affect momentum?
• How can acceleration change the motion of an object?
• What is an acceleration vs time graph?
• What are some examples of acceleration?
• What are some examples of relative velocity?
• What are some examples of relative speed?
• What is relative speed?
• What is relative motion?
• Question #484e1
• A Boeing 474 passenger airliner cruises at a speed of 907km/hr. If the plane reaches cruising speed headed due east and then encounters a headwind of 14km/hr, what is the plane's actual speed?
• In the figure here, block 1 of mass 2.3 kg and block 2 of mass 3.2 kg are connected by a string of negligible mass and are initially held in place. Block 2 is on a frictionless surface tilted at θ = 29 ˚ ?
• Objects A and B are at the origin. If object A moves to #(2 ,1 )# and object B moves to #(5 ,2 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(2 ,3 )# and object B moves to #(5 ,2 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(2 ,3 )# and object B moves to #(5 ,8 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-2 ,7 )# and object B moves to #(5 ,3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(6 ,7 )# and object B moves to #(-1 ,3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(6 ,2 )# and object B moves to #(-1 ,1 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• 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?
• Objects A and B are at the origin. If object A moves to #(-5 ,-3 )# and object B moves to #(-1 ,-8 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(0 ,-3 )# and object B moves to #(-1 ,-8 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(0 ,-1 )# and object B moves to #(9 ,6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(3 ,-4 )# and object B moves to #(2 ,-6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-4 ,-4 )# and object B moves to #(2 ,-6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-4 ,7 )# and object B moves to #(2 ,-3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-4 ,7 )# and object B moves to #(5 ,-3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-2 ,7 )# and object B moves to #(3 ,-3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-2 ,8 )# and object B moves to #(3 ,-3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-2 ,8 )# and object B moves to #(-5 ,-6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-2 ,2 )# and object B moves to #(-5 ,-6 )# over #2 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-7 ,2 )# and object B moves to #(-5 ,-6 )# over #2 s#, what is the relative velocity of object B from the perspective of object A?
• Objects A and B are at the origin. If object A moves to #(-7 ,2 )# and object B moves to #(-5 ,-6 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(-7 ,5 )# and object B moves to #(-5 ,-2 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(8 ,5 )# and object B moves to #(9 ,-2 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(8 ,6 )# and object B moves to #(9 ,-2 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(-1 ,6 )# and object B moves to #(6 ,-2 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(-1 ,6 )# and object B moves to #(6 ,-12 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,6 )# and object B moves to #(6 ,0 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,7 )# and object B moves to #(6 ,0 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,7 )# and object B moves to #(6 ,-5 )# 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.
• Objects A and B are at the origin. If object A moves to #(-2 ,7 )# and object B moves to #(6 ,-5 )# 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.
• Objects A and B are at the origin. If object A moves to #(-2 ,7 )# and object B moves to #(7 ,-5 )# 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.
• Objects A and B are at the origin. If object A moves to #(-2 ,2 )# and object B moves to #(7 ,-5 )# 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.
• Objects A and B are at the origin. If object A moves to #(-2 ,2 )# and object B moves to #(7 ,9 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-5 )# and object B moves to #(7 ,9 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-5 )# and object B moves to #(-1 ,9 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,-5 )# and object B moves to #(-1 ,4 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-5 )# and object B moves to #(-1 ,4 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-5 )# and object B moves to #(-1 ,12 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-5 )# and object B moves to #(-5 ,12 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-3 )# and object B moves to #(-5 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-2 )# and object B moves to #(-5 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,-2 )# and object B moves to #(-5 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,7 )# and object B moves to #(-6 ,-4 )# 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.
• 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.
• Objects A and B are at the origin. If object A moves to #(9 ,7 )# and object B moves to #(-8 ,-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.
• Objects A and B are at the origin. If object A moves to #(9 ,7 )# and object B moves to #(-8 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(9 ,7 )# and object B moves to #(-4 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,-8 )# and object B moves to #(-4 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,-8 )# and object B moves to #(-4 ,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.
• Objects A and B are at the origin. If object A moves to #(5 ,-8 )# and object B moves to #(-4 ,2 )# 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.
• Objects A and B are at the origin. If object A moves to #(5 ,-3 )# and object B moves to #(-7 ,2 )# 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.
• Objects A and B are at the origin. If object A moves to #(5 ,-1 )# and object B moves to #(-7 ,2 )# 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.
• Objects A and B are at the origin. If object A moves to #(5, -1)# and object B moves to #(-7, 8)# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-1 )# and object B moves to #(-7 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,5 )# and object B moves to #(-6 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,1 )# and object B moves to #(-6 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,1 )# and object B moves to #(-6 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,1 )# and object B moves to #(12 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,7 )# and object B moves to #(1 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,7 )# and object B moves to #(1 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,7 )# and object B moves to #(1 ,-4 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,6 )# and object B moves to #(1 ,-4 )# 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.
• 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.
• Objects A and B are at the origin. If object A moves to #(3 ,7 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,7 )# and object B moves to #(6 ,-2 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,7 )# and object B moves to #(6 ,-7 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,-2 )# and object B moves to #(6 ,-7 )# 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.
• Objects A and B are at the origin. If object A moves to #(-8 ,-2 )# and object B moves to #(5 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(-5 ,-1 )# and object B moves to #(5 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(-6 ,-2 )# and object B moves to #(5 ,4 )# 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.
• Objects A and B are at the origin. If object A moves to #(0 ,4 )# and object B moves to #(9 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(0 ,-3 )# and object B moves to #(9 ,-3 )# 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.
• Objects A and B are at the origin. If object A moves to #(5 ,-3 )# and object B moves to #(9 ,7 )# 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.
• Objects A and B are at the origin. If object A moves to #(5 ,-7 )# and object B moves to #(7 ,4 )# 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.
• Objects A and B are at the origin. If object A moves to #(5 ,-7 )# and object B moves to #(7 ,4 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(4 ,-3 )# and object B moves to #(7 ,4 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(4 ,-1 )# and object B moves to #(7 ,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.
• Objects A and B are at the origin. If object A moves to #(5 ,-1 )# and object B moves to #(-8 ,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.
• Objects A and B are at the origin. If object A moves to #(5 ,-1 )# and object B moves to #(-8 ,6 )# 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.
• Objects A and B are at the origin. If object A moves to #(9 ,-7 )# and object B moves to #(-8 ,6 )# 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.
• Objects A and B are at the origin. If object A moves to #(-9 ,-4 )# and object B moves to #(-3 ,6 )# 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.
• Objects A and B are at the origin. If object A moves to #(-7 ,4 )# and object B moves to #(-3 ,2 )# 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.
• Objects A and B are at the origin. If object A moves to #(-7 ,3 )# and object B moves to #(-6 ,2 )# 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.
• Objects A and B are at the origin. If object A moves to #(-7 ,3 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-8 )# and object B moves to #(-2 ,-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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-8 )# and object B moves to #(1 ,-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.
• Objects A and B are at the origin. If object A moves to #(-3 ,-8 )# and object B moves to #(1 ,-1 )# 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.
• Objects A and B are at the origin. If object A moves to #(-7 ,-5 )# and object B moves to #(1 ,-1 )# 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.
• Objects A and B are at the origin. If object A moves to #(-7 ,-9 )# and object B moves to #(1 ,-1 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,-9 )# and object B moves to #(1 ,-1 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,-9 )# and object B moves to #(1 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,-9 )# and object B moves to #(5 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(-4 ,-3 )# and object B moves to #(5 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(0 ,-3 )# and object B moves to #(5 ,8 )# 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.
• Objects A and B are at the origin. If object A moves to #(0 ,-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.
• 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.
• Objects A and B are at the origin. If object A moves to #(4 ,-2 )# and object B moves to #(2 ,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.
• Objects A and B are at the origin. If object A moves to #(3 ,1 )# and object B moves to #(2 ,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.
• Objects A and B are at the origin. If object A moves to #(3 ,-4 )# and object B moves to #(2 ,7 )# 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.
• 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.
• Objects A and B are at the origin. If object A moves to #(6 ,-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.
• Objects A and B are at the origin. If object A moves to #(3 ,-5 )# 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.
• Objects A and B are at the origin. If object A moves to #(3 ,-7 )# and object B moves to #(2 ,9 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
• Objects A and B are at the origin. If object A moves to #(1 ,-1 )# and object B moves to #(5 ,9 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
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