A particle is projected up an inclines plane. Plane is inclined at an angle `theta` with horizontal and particle is projected at an angle `alpha` with horizontal. If particle strikes the plane horizontally prove that `tan alpha=2 tan theta`

Explanation

To prove that \( \tan \alpha = 2 \tan \theta \) when a particle is projected up an inclined plane and strikes it horizontally, we can follow these steps:

### Step 1: Understand the Problem
We have a plane inclined at an angle \( \theta \) to the horizontal, and a particle is projected at an angle \( \alpha \) to the horizontal. The particle strikes the inclined plane horizontally.

### Step 2: Analyze the Point of Impact
When the particle strikes the plane horizontally, it means that at the point of impact, the vertical component of its velocity is zero. This occurs when the particle reaches its maximum height.

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