Short Answer 
The process to analyze the movement of a block down an inclined plane involves identifying forces such as gravity, normal force, and kinetic friction. By calculating the work done by these forces, one can use the work-energy principle to determine the distance traveled by the block on the horizontal surface, which is found to be approximately 17.937 meters.
Step 1: Identify the Forces Acting on the Block
First, we need to recognize the main forces acting on the block as it moves down the inclined plane and onto the horizontal surface. These forces include:
- Gravity: This force pulls the block down, with components both parallel and perpendicular to the incline.
- Normal Force: Acts perpendicular to the surface of the inclined plane, balancing the perpendicular force of gravity.
- Kinetic Friction: This force opposes the motion both on the incline and the horizontal surface.
Step 2: Calculate Work Done by Each Force
Next, establish the work done by each force to find the kinetic energy gained by the block. Use the work-energy principle, which can be summarized as:
- Work of Gravity: Calculated using the height and the sine of the angle of inclination.
- Work of Friction on the Inclined Plane: Determined through the kinetic friction formula, involving the normal force.
- Work of Friction on the Horizontal Surface: Calculated similarly, based on the coefficient of friction specific to the horizontal surface.
Step 3: Solve for Distance Traveled After the Inclined Plane
Finally, substitute the values obtained from the previous calculations into the work-energy equation to solve for the distance (d) traveled on the horizontal surface. Steps include:
- Insert known values into the work equation.
- Rearrange the equation to solve for distance (d).
- Upon solving, you find that the block travels approximately 17.937 meters after leaving the inclined plane.