It is due to the momentum of the two bodies.
If you jump up, for example, with a momentum of 100 kilogram x meter / second (this can be done by jumping up at a speed of 2 meters/second, if you have a mass of 50 kilograms), then the Earth will recoil by the same amount of momentum - in the opposite direction of course. This follows directly from Conservation of Momentum.
For different observers (moving at different velocities), the object will have different velocities (relative to the corresponding observer). For one and the same observer, the body will have only one velocity at any given time.
Relative location.
Simply because physicists discovered that it is a product that is conserved. In collisions of two objects for example, if you add up the momentum before the collision the momentum will be the same after the collision. Note that momentum is not something that has a concrete reality. A rock sitting on the ground has zero momentum relative to us here on earth but has alot of momentum relative to someone on mars. It can not have zero momentum and alot of momentum at the same time, it depends on ones frame of reference. My point is that momentum is not at 'concrete" thing. Refer to the 'Conservation of linear momentum' in Wikipedia.org, "The World's Encyclopedia" *Check out related links*
they are relative because of the comets tail. opposite the sun. so they are relative upward
Most velocities are measured relative to Earth.Most velocities are measured relative to Earth.Most velocities are measured relative to Earth.Most velocities are measured relative to Earth.
Depending on how you define it. Momentum is always given positive units, but sometimes when considered in a relative view, it can be in a negative direction making the overall value negative too (while mass is always positive, velocity might be in a negative direction where e.g. two masses are moving in opposite directions).
If you jump up, for example, with a momentum of 100 kilogram x meter / second (this can be done by jumping up at a speed of 2 meters/second, if you have a mass of 50 kilograms), then the Earth will recoil by the same amount of momentum - in the opposite direction of course. This follows directly from Conservation of Momentum.
orrery
For different observers (moving at different velocities), the object will have different velocities (relative to the corresponding observer). For one and the same observer, the body will have only one velocity at any given time.
impulse (force x time) is equal to momentum (mass x velocity); Ft=mv
Momentum is related to velocity and mass. When an object's velocity is zero relative to its surroundings, it has no momentum. Therefore it is untrue to say that an object never looses its momentum.
Vector addition of velocities would be if something like you were on an escalator, which is going down, and you tried to run up the escalator. So if the escalator is moving down at a rate of 5 ft/sec and you run up at 13 ft/sec (relative to the escalator) then the net velocity relative to the Earth is 8 ft/sec up. So you just subtract, because the two vectors are in the same line. OK so really the direction is at an angle (rather than 'up'). The larger velocity direction will determine the net direction. If you were walking up the escalator at 3 ft/sec (relative to the escalator), then your net velocity is 2 ft/sec down.
relative, opposite of absolute
its not possible.. momentum is always conservedYou could say that momentum, in its classical definition, is not conserved at relativistic velocities. Momentum is conserved at relativistic speeds if momentum is redefined as; p = γmov where mo is the "rest (invariant) mass" and γ is the Lorentz factor, which is equal to γ = 1/√(1-ʋ2/c2) and ʋ is the relative velocity. Some argue that the relativistic mass, m' = γmo, is unnecessary, in which case the proper velocity,defined as the rate of change of object position in the observer frame with respect to time elapsed on the object clocks (its proper time) can be used.Proper velocity is equal to v = γʋ, so p = mov. mo here is the invariant mass, where before it represented the "rest mass."The problem with Newton's p = mv, is that with this definition, the total momentum does not remain constant in all isolated systems, specifically, when dealing with relativistic velocities. Mass and or velocity is dependent on the relative velocity of the observer with respect to the isolated system.It is important to add that with this new definition momentum is conserved. With that said, my point is not to argue that momentum is not always conserved but to simply offer an explanation for the relatively (no pun intended) common statement "momentum is not conserved in ALL isolated systems" which could be where the original question stems from.
If the velocities are equal from my point of view, then I see them both moving at the same speed and in the same direction. That means that from the point of view of an observer riding on either body, the other one is standing still. Their relative velocity is zero. This is exactly the situation with a passenger and the book she's reading, both in an airliner flying west at 400 mph.
Relative location.