Problem 274. Bouncing disk

@Dyuman I agree that the problem description could be MUCH improved... see solution 14777825 for a better explanation (and a detailed solution development).

As for friction: friction happens as the "disk" (really dimensionless, as Rafael pointed out) moves about in the rectangular "room". Bounces at any room boundary are frictionless.

Hopefully the following is a better problem description:
Problem 274. Bouncing Disk (Refined Statement)
A point‑like disk moves inside a rectangular room of width a and height b.
The disk starts at position (x_0, y_0) with an initial speed V (m/s). Its initial velocity makes an angle φ (radians) with the positive x‑axis.
The disk experiences a constant friction factor ν > 0, which causes its speed to decay until it eventually stops. The effective travel distance before coming to rest is finite and given by:
D = \frac{V^2}{2 g \, \nu}
where g \approx 9.80665 \,\text{m/s}^2 is the gravitational acceleration constant.
(This formula reflects the way the original Cody problem defines the friction law.)
The disk moves in straight lines until it collides with a wall. Collisions are perfectly elastic:
- At a vertical wall, the x‑component of velocity reverses sign.
- At a horizontal wall, the y‑component of velocity reverses sign.
No energy is lost in collisions; only the friction factor reduces the total travel distance.
Task:
Simulate the motion until the disk has traveled the full path length D. Return the final coordinates (x, y) of the disk.
Input arguments:
- x0, y0 — initial coordinates of the disk (meters)
- V — initial speed (m/s)
- phi — initial angle relative to the x‑axis (radians)
- a, b — room dimensions (meters)
- nu — friction factor (> 0)
Output:
- x, y — final coordinates of the disk (meters)
Accuracy requirement:
The result must be correct within a tolerance of 10^{-3}.

Problem 274. Bouncing Disk (Formal Restatement)
Consider a point‑like disk moving inside a rectangular domain of width a and height b. The disk is initially located at position (x₀, y₀) and is launched with speed V (m/s). The initial velocity vector makes an angle φ (radians) with the positive x‑axis.
The disk experiences a constant friction factor ν > 0, which causes its speed to decay until it comes to rest. The effective travel distance before stopping is finite and given by
D = V² / (2 g ν),
where g ≈ 9.80665 m/s² is the gravitational acceleration constant.
The disk moves in straight lines until it collides with a boundary. Collisions are perfectly elastic:
- At a vertical wall, the x‑component of velocity reverses sign.
- At a horizontal wall, the y‑component of velocity reverses sign.
No energy is lost in collisions; only the friction factor reduces the total travel distance.
Task: Determine the final position (x, y) of the disk after it has traveled the full distance D.
Inputs:
- x₀, y₀ — initial coordinates of the disk (meters)
- V — initial speed (m/s)
- φ — initial angle relative to the x‑axis (radians)
- a, b — dimensions of the rectangular room (meters)
- ν — friction factor (> 0)
Output:
- x, y — final coordinates of the disk (meters)
Accuracy requirement: The result must be correct within a tolerance of 10⁻³.