How do i calculate an object's velocity along a vector?

[Nanako]

assuming 3D space. i have an object moving in a fairly arbitrary direction. Say it's being fired in an arc, and it hits a wall.

What i want to find out is, how much of that object's velocity is "toward" the wall. Ie, if i define a direction from the object to the wall, how do i calculate its velocity in that direction

i could swear I've done this before, but i have only vague inklings left.
is vector projection what I'm looking for?

 

[siddharth23]

assuming 3D space. i have an object moving in a fairly arbitrary direction. Say it's being fired in an arc, and it hits a wall.

What i want to find out is, how much of that object's velocity is "toward" the wall. Ie, if i define a direction from the object to the wall, how do i calculate its velocity in that direction

i could swear I've done this before, but i have only vague inklings left.
is vector projection what I'm looking for?

You need to resolve the velocity vector into two vectors! One towards the wall (perpendicular to the wall) and one parallel to the wall. You'll need to know the angle of velocity for that.
How can you do that?

 

[Nanako]

i'm afraid i have no idea. I'm probably wrong, but to me that sounds like a tiny modification of the same problem

what exactly do you mean the angle of the velocity? as defined in radians or degrees relative to world up?

 

[brainpushups]

Yes. The vector projection would work and would be the most general way to describe the direction of the velocity in relation to the direction of the wall. If the wall has a definite orientation (say, the y direction) and you know the angle that the velocity vector makes with respect to the position vector of the wall then siddarth23's suggestion is certainly the simplest way to express this component of the velocity.

 

[Nanako]

thank you. it turns out unity already has a native function to do this for me http://docs.unity3d.com/ScriptReference/Vector3.Project.html

i'll use that, but i;m still curious about the math behind it. i shall research that a little

 

[DrStupid]

Ie, if i define a direction from the object to the wall, how do i calculate its velocity in that direction

If v is the velocity and n the normal vector than

\vec v_n = \vec n \cdot \frac{{\vec n \cdot \vec v}}{{\vec n^2 }}

is the normal component of the velocity.

 

[siddharth23]

Try reading up on resolution of vectors.
http://www.physicsclassroom.com/class/vectors/Lesson-1/Vector-Resolution

Basically, any vector can be resolved into two components whose addition give the original vector.