''there are also component and computation vectors which we construct to help with calculations and understanding.''

can you please expand this?

Let's take your example:

we can plot a curve from a-b, and calculate speed over distance etc, we can use the ground to define a plane, and place points at different heights to represent the curve.

You are using the ground as a reference plane and perpendicular to that a line representing height.

Let's say at a particular point your ball has a velocity of 14 units, 45° upwards.

We can imagine that this velocity vector is composed of 2 vectors (component vectors) one parallel to the ground plane and one upwards. If you use right angled triangles you can work out that each has a magnitude of almost 10 units. So this tells us how fast your ball is rising vertically and how fast it is travelling horizontally (at that point in time).

You can do the same with forces, even though the forces are stationary eg reaction forces, and don't represent any trajectory.

Useful?

I had to look up transitory, the thing is with all vectors in my opinion, they are never really there and it is a bit like dot to dot, i.e a cannon balls curvature path.

But the movement, velocity and forces are real. We are only using numbers, lines, angles, coordinates as a way of describing what is happening.

Some of the vectors have a very real effect.

Let's say you are in a boat with no wind, if the boat moves forward you will feel a wind in your face, but there is no wind blowing! We can describe that apparent wind with a vector of equal magnitude to the boat speed but in the opposite direction to that of travel.

Now let's add a real wind blowing at 90° over the side of the boat, let's say for convenience that the wind is equal to the boat speed. You don't feel 2 winds blowing, one from the side and one from the front, you feel a single wind blowing from 45° between ahead and the side. This wind is very

*real* even though it is termed the apparent wind, and it is the resultant of the 2 wind vectors, one from ahead the other from the side.