A body is projected up with a speed `v_0` along the line of greatest slope of an inclined plane of angle of inclination `beta`. If the body collides elastically perpendicular to the inclined plane, find the time after which the body passes through its point of projection.

Explanation

To solve the problem, we need to analyze the motion of a body projected up an inclined plane and determine the time after which it returns to its point of projection after an elastic collision. Here’s a step-by-step solution:

### Step 1: Understand the Motion Components
The body is projected with an initial speed \( v_0 \) along the inclined plane, which makes an angle \( \beta \) with the horizontal. We need to resolve the motion into two components: parallel to the inclined plane (x-direction) and perpendicular to the inclined plane (y-direction).

### Step 2: Resolve Initial Velocity
- The component of the initial velocity along the inclined plane (x-direction) is:
\[
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