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: Understand the Energy Conservation Principle
The total mechanical energy of the disk will be conserved as it rolls up the ramp. Initially, the disk has kinetic energy (both translational and rotational) and no potential energy. As it rolls up the ramp, this kinetic energy is converted into potential energy until it comes to a stop.

### Step 2: Write the Energy Equations
1. **Initial Kinetic Energy (KE_initial)**:
The total kinetic energy of the disk can be expressed as:
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