Prove that the maximum horizontal range is four times the maximum height attained by the projectile, when fired at an inclination so as to have maximum horizontal range.

Explanation

To prove that the maximum horizontal range (R) is four times the maximum height (H) attained by the projectile when fired at an inclination that gives maximum horizontal range, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Range Formula**:
The formula for the range (R) of a projectile launched at an angle θ with an initial velocity u is given by:
\[
R = \frac{u^2 \sin(2\theta)}{g}
...