Exploring the Purpose of Resultant Velocity in 2D Motion

[mmegdill]

I have a pretty simple question: What is the purpose of a resultant velocity in 2D motion? Is it used for anything besides finding the vertical and horizontal components?

For example, I was given this problem:

Sharron dives off a spring board into the pool 3m below with a velocity of 8 m/s at an angle of 80° to the horizontal. What are the vertical and horizontal components of her velocity? What height does she reach before beginning her descent? How far from the spring board horizontally does she hit the water?

I can solve this problem without difficulty, but it got me wondering what the point of her 8m/s velocity is. Is it used for anything ever?

 

[CompuChip]

The resultant velocity is in a sense the "physical" unit.
When you are driving in your car, a lot of forces are acting on you (the wind, your engine, friction from the road and the air). Your speedometer showing 50 km/h (or mi/h, depending on where you live :-)) is giving you the resultant velocity though: the effect of everything combined into the actual velocity with which you move relative to the road.

So I would turn it around and say that actually the decomposition is only for calculational purposes and the resultant is the relevant quantity.

 

[robphy]

To add to CompuChip's reply...
Note that the "components of the velocity [or any vector, in general]" depend on your choice of coordinate axes. You get different numerical values for the components with a different set of axes. However, the magnitude of the vector will the same, regardless of what axes you choose.

When you study "kinetic energy", you'll see that the speed (the magnitude of the velocity) is featured... not the components [although these can be used to calculate the speed].

By the way...
When I think of "resultant velocity", I think of combining the effects of two velocities... suppose I walk with some velocity in a train car, which itself is moving over the ground... How fast am I moving with respect to the ground?