The surface of a hill is inclined at an angle `alpha` to the horizontal .A stone is thrown from the summit of the hill at an angle `beta` to the vertical with velocity `v_0`.How far from the summit will the stone strike the ground ?

Explanation

To solve the problem of how far from the summit of the hill the stone will strike the ground, we can break it down into several steps:

### Step 1: Understand the Setup
We have a hill inclined at an angle \( \alpha \) to the horizontal. A stone is thrown from the summit at an angle \( \beta \) to the vertical with an initial velocity \( v_0 \). We need to find the horizontal distance from the summit where the stone lands on the inclined plane.

### Step 2: Resolve the Initial Velocity
The stone is thrown at an angle \( \beta \) to the vertical, which means the angle with respect to the inclined plane is \( \theta = 90^\circ - \alpha - \beta \). We can resolve the initial velocity \( v_0 \) into two components:
- **Vertical Component**: \( v_{0y} = v_0 \cos(\beta) \)
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