Relative velocity
The velocity of one object as seen from another moving object. You add or subtract velocity vectors.
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Analogy
Walking forward on a moving train: the platform sees your speed plus the train's.
Example
Across: 4 m/sDownstream: 3 m/sspeed = sqrt(16 + 9) = 5 m/s
In practice
A boat steers 4 m/s straight across a river flowing 3 m/s. Its speed over the ground is 5 m/s.
Questions people ask
How do I find the velocity of A relative to B?
Subtract B's velocity from A's velocity as vectors. This gives what a person riding along with B would see for A. If two cars move at 30 and 20 m/s in the same direction, the faster car moves at 10 m/s relative to the slower one.
Why does rain look slanted from a moving car?
The rain falls straight down relative to the ground, but you also move forward. Relative to you, the rain has a backward velocity equal to your speed added as a vector. The faster the car goes, the more slanted the rain looks.