A particle of mass 0.2 kg has an intial speed of `5 ms^(-1) ` at the bottom of a rough inclined plane of inclination `30^(@)` and vertical height 0.5 m . What is the speed of the particle as it reaches the top of the inclined plan ? (Take `mu = 1//sqrt3 , g = 10 ms^(-2)` ) .

Explanation

To solve the problem step by step, we will analyze the motion of the particle on the inclined plane, taking into account the forces acting on it.

### Step 1: Determine the length of the incline (AB)
Given the vertical height (h) of the inclined plane is 0.5 m and the angle of inclination (θ) is 30°.

Using the relationship:
\[
\text{Length of incline (AB)} = \frac{h}{\sin \theta}
...