1 kg particle at a height of 4 m has a speed of 2 m/s down a incline making an angle `53^@` with horizontal as shown in figure. It slides on a horizontal section of length 3 m at ground level and then up an incline making an angle `37^@` with horizontal. All surfaces have `mu_k=0.5`. How far from point O (bottom of right inclined plane), along the incline making and angle `37^@` with horizontal, does the particle first come to rest?

Explanation

To solve the problem, we will apply the work-energy theorem and analyze the motion of the particle step by step.

### Step 1: Calculate the initial potential energy (PE) and kinetic energy (KE) of the particle at the height of 4 m.

The potential energy at height \( h \) is given by:
\[ PE = mgh \]
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