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Relative Velocity

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The velocity of one object or material relative to another

Used in the calculation of fluid drag

Involves the subtraction of velocity vectors

- EXAMPLE 1: Two runners are in a race. Runner A is traveling at a velocity of 7 m/s (vA=7 m/s) while runner B is traveling at a velocity of 7.5 m/s (vB=7.5 m/s) in the same direction. What is their relative velocity?
The relative velocity equals the difference between their velocities.

Relative Velocity = vB – vA = 7.5 m/s – 7 m/s = .5 m/s

This means that B is moving away from A at a velocity of .5 m/s

- Example 2: The two runners in the previous problem are approaching each other (that is, their velocity vectors are in opposite directions). In this case vA=-7 m/s while vB=7.5 m/s.
Relative Velocity = vB – vA = 7.5 m/s – (-7 m/s) = 14.5 m/s

This is also called a closing velocity (it’s the velocity that results from two objects closing on each other).

- This relates to the velocity of a fluid medium (like air or water) compared to an object moving within it.
EXAMPLE 1: A runner is moving at a velocity of 7 m/s (vR = 7 m/s) and experiences a headwind of 3 m/s (vw = -3 m/s) (Since it’s a headwind it’s opposite in direction to the runner’s velocity) . What’s the relative wind velocity?

Relative Wind Velocity = vR – vw = 7 m/s – (-3 m/s) = 10 m/s

This produces the same effect as the runner standing still and facing into a wind that’s blowing at 10 m/s.

EXAMPLE 2: A runner is moving at a velocity of 7 m/s (vR = 7 m/s) and experiences a tailwind of 3 m/s (vw = 3 m/s) (Since it’s a tailwind it’s in the same direction as the runner’s velocity) . What’s the relative wind velocity?

Relative Wind Velocity = vR – vw = 7 m/s – 3 m/s = 4 m/s