A solid disk is rolling without slipping on a level surface at a constant speed of `2.00m//s`. How far can it roll up a `30^(@)` ramp before it stops? (take `g=9.8m//s^(2))`

Explanation

To solve the problem of how far a solid disk can roll up a 30-degree ramp before it stops, we will use the principle of conservation of energy. Here's a step-by-step solution:

### Step 1: Identify Initial Energy
The initial energy of the disk consists of its kinetic energy, as it starts rolling on a level surface. The total kinetic energy (KE) is the sum of translational kinetic energy (TKE) and rotational kinetic energy (RKE).

The translational kinetic energy is given by:
\[
\text{TKE} = \frac{1}{2} m v^2
...