Calculating Velocities After Reflection

[Sidelines]

So here's my problem... I have a particle traveling at velocity T, Vt, with components Velocity x, Velocity y, and Velocity z (3 dimensions).
This particle collides with a triangular surface. Each point of the triangle is known (x y and z for each point)
I would like to find the components of the velocity after the particle reflects off the triangle surface. (no velocity is lost so Vt remains the same)
Knowing these three points I found a vector that follows the normal angle off the surface.
You could take this vector and find the normal angle.

Known Variables:
Vt, Overall velocity
Vx, Vy, Vz, velocity components of Vt
P1, P2, P3, points of triangle (x,y,z)
Normal Vector off the surface (x,y and z components)

You could possibly find the normal angles for Z and XY, but if there's a way to do it without Sin, Cos, Tan, it would make things much easier.

Any help is appreciated as I've been stuck on this for a long time.

 

[Drakkith]

You could try the homework section. They might be able to help you there.

 

[Sidelines]

Yeah I suppose I could. This isn't for homework, but oh well

 

[Drakkith]

Yeah, I would help you if I could, but I'm still confused on why you need any more information other than the angle of impact.

 

[sardar]

I understand your problem and can provide some suggestions to help you solve it. First, let's review the basics of velocity and reflection. Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude (speed) and direction. When a particle reflects off a surface, its direction of motion changes, but its speed remains the same.

To calculate the velocity after reflection, we need to consider the laws of reflection. These laws state that the angle of incidence (the angle between the incoming particle's velocity and the surface normal) is equal to the angle of reflection (the angle between the outgoing particle's velocity and the surface normal). This means that the direction of the reflected velocity can be determined by finding the angle of incidence and then reflecting it across the surface normal.

Now, let's apply this to your problem. We know the velocity components of the particle before reflection (Vx, Vy, Vz) and the normal vector of the surface (Nx, Ny, Nz). To find the angle of incidence, we can use the dot product between the two vectors:

cos(theta) = (VxNx + VyNy + VzNz) / (|V| * |N|)

Where theta is the angle of incidence and |V| and |N| are the magnitudes of the velocity and normal vectors, respectively.

Next, we can use the cross product between the velocity vector and the normal vector to find the axis of rotation for the reflection. This will give us a vector perpendicular to the surface, which we can then use to reflect the angle of incidence:

R = V x N

Finally, we can use the axis of rotation and the angle of incidence to calculate the reflected velocity using a rotation matrix:

V' = V*cos(theta) + (R x V)*sin(theta) + R*(R x V)*(1-cos(theta))

Where V' is the reflected velocity and the * represents vector multiplication.

I understand that this may seem complex, but it is a common method used in physics and mathematics to calculate reflections in multiple dimensions. If you are not familiar with these concepts, I suggest seeking out resources on vector operations and rotations to better understand the process.

I hope this helps you solve your problem and if you have any further questions, don't hesitate to ask. As scientists, we are always here to help and support each other in our pursuit of knowledge and understanding. Keep up the