Two inclined planes (AB) and (BC) are placed as shown in Fig. 2 (ABC).3 A particle is projected from the foot of the plane of angle ` alpha` along its line witn a velocity just sufficient to carry it to the top after which the particle slides down the other inclined plane. Fing the total time it will take to reach the pont (C ).

Explanation

To solve the problem of finding the total time it takes for a particle projected from the foot of an inclined plane (AB) to reach point C after sliding down the second inclined plane (BC), we can break the problem into two parts: the time taken to ascend the first inclined plane and the time taken to descend the second inclined plane.

### Step 1: Analyze the motion on the first inclined plane (AB)

1. **Identify the parameters**:
- Let the angle of inclination of plane AB be α.
- Let the height of plane AB be h.
- The initial velocity \( u \) is just sufficient to reach the top, which means at the top, the final velocity \( v = 0 \).
...