Question

Prove that Vab vector=Va vector-Vb vector

Answer 1

relative velocity is generally associated with an object moving through a fluid – a fluid being defined as
any substance that tends to flow or continuously deform when acted on by a shear force. However,
relative velocity can also be calculated between two bodies. The relative velocity of a body is the velocity
as it approaches or recedes another body, where one or both of the bodies are in motion. As velocity is a
vector quantity, it is both magnitude and direction sensitive. The sign attached to the relative velocity
indicates the direction of the relative velocity with respect to reference direction. Relative velocity refers
to two moving bodies; it is not just the difference in the velocities.
Magnitude of the relative velocity of bodies moving in opposite directions to each other, i.e. moving
closer together or further apart , is calculated as the algebraic sum of the speeds of the
two bodies, remembering that they are direction aware and that in this case at least one of the values is
travelling in a negative direction. Magnitude of the relative velocity of bodies moving in the same
direction is the difference in the speeds of body A and body B. If two bodies are moving in the
same direction at the same velocity, then the relative velocity will be zero.
The equation for relative velocity is as follows:
VAB = VA – VB
Where:
VAB = is the velocity of body A as observed by body B
VA = velocity of body A
VB = velocity of body B
(alternatively, this can be switched around to find VBA, which is the velocity of body B relative to body A.
This will result in the same value as VAB but in the opposite direction.