A wooden block is kept on a polished wooden plank and the inclination of the plank is gradually increased. It is found that the block starts slipping when the plank makes an angle of `18^@` with the horizontal. However, once started the block can continue with uniform speed if the inclination is reduced to `15^@`. Find the coefficients of static and kinetic friction between the block and the plank.

Explanation

To solve the problem, we need to find the coefficients of static and kinetic friction between the wooden block and the polished wooden plank based on the given angles of inclination.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- When the block is on the inclined plank, it experiences two main forces: the gravitational force acting downwards (mg) and the normal force acting perpendicular to the surface of the plank.
- The gravitational force can be resolved into two components:
- Perpendicular to the incline: \( mg \cos \theta \)
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