OK, so I have a golf-ish game where there is a ball that moves around the screen with separate x and y velocities which vary based on an angle chosen before the ball is hit. This all works perfectly fine, the ball bounces off the walls, etc. But when I try to apply friction to the ball's movement, I encounter some issues.

The process I am using to scale down my velocity vector while maintaining the same angle of motion is as follows:
   1. Find the magnitude of the vector
   2. Normalize the vector
   3. Decrease the value of the magnitude by a friction constant
   4. Multiply x and y velocity components by the new magnitude
My code looks like this:
.PUTTPUTT
P*16**cos(θ)->V             //P represents power, used to determine how fast the ball will move
P*16**sin(θ)->W             //V is the X-velocity; W is the Y-velocity
Repeat getKey(15)
 Pt-On(X+V->X/256, Y+W->Y/256, Pic0)     //X and Y are the position components
 127*W//sin(tan-1(V,W))->M               //M is the magnitude of the velocity vector
 M-F*W//M->W                //F is the friction constant. I multiply the new magnitude by each component before dividing by the current magnitude
 M-F*V//M->V                //because W//M would give a value of 0
 If X/256>90
  -V->V
 End
 If Y/256>59
  -W->W
 End
 DispGraphClrDraw
End
Depending on P and θ, the code may or may not work, and I can't figure out why; the ball does seemingly random stuff, often not even going in the right direction.
Also, I don't know if this is relevant, but when I debugged the magnitude, it changed whenever the ball bounced off the left or right of the screen, which I don't think should be happening.
Can anybody help me fix this?

Awesome, it works and makes sense now!

I'm attempting to access arbitrary OS vars from the calculator, and subsequently delete them. The code works with programs, groups, appvars, and letters, but whenever I try to access the vars represented by tokens, it does not work properly. Basically, I copy the randomly selected var name over into another string so that I can delete it, but the string doesn't seem to recognize the tokens following the first one. Here is my code (simplified):
.DELSUB2
Fix 5
"var "->Str3
"ABCDEFGHIJKLMNOPQRSTUVWXYZØ"->Str5
"L1L2L3L4L5L6"->Str6
"  "->Str8
sub(LSD)
Return

Lbl LSD                             //This will only ever delete L1. If the randomly selected number is not 0, then nothing will happen
Copy(rand^6*2+Str6,Str8,2)
DelVar Str8
Return

Lbl ABC                             //This works
Copy(rand^27+Str5,Str3+1,1)
DelVar Str3
Is there a way to get around this lack of string support for tokens? Like, can these variables be accessed via hex code or something? Thank you!

When your teacher gets mad and threatens to take your calc because you always give everybody in the class games, so you say they're all educational and math-oriented, and ask if she wants them for her calc. She accepts, and you speedily use the very unstable Axe 1.0.1 to make a nasty virus with a math-ish name, and crash her calc and she gets really mad... 

True story

I linked my TI84 Plus and a TI84 Plus SE together and it works perfectly. The synchronization was almost instantaneous and the game played just fine. It was quite enjoyable. 

If I could figure out how to take multiple calc screenshots, I'd post them... But great job on the game!

Wow! Thanks so much. I am "buying" them right now.