A gun is fired from a moving platform and the ranges of theshot are observed to be R and S when platform is moving forward or backward respectively with velocity v prove that the elevation of the gun is
`tan ^(-1)[(g(R-S)^(2))/(4V^(2)(R+S))]`

Explanation

To solve the problem, we need to analyze the motion of the gun fired from a moving platform. We will derive the expression for the elevation angle of the gun based on the ranges observed when the platform is moving forward and backward.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let the velocity of the platform be \( v \).
- When the platform moves forward, the range of the shot is \( R \).
- When the platform moves backward, the range of the shot is \( S \).
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