A solid sphere rolls up a plane inclined at `45^(@)` to the horizontal. If the speed of its centre of mass at the bottom of the plane is 5 m/s , find how far the sphere travels up the plane.

Explanation

To solve the problem of a solid sphere rolling up an inclined plane at an angle of \(45^\circ\) with an initial speed of \(5 \, \text{m/s}\), we can use the principles of energy conservation and kinematics. Here’s a step-by-step solution:

### Step 1: Identify the Given Data
- Initial speed of the center of mass, \(v = 5 \, \text{m/s}\)
- Angle of inclination, \(\theta = 45^\circ\)
- Acceleration due to gravity, \(g = 9.8 \, \text{m/s}^2\)

### Step 2: Determine the Acceleration of the Sphere
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