A projectile is launched at an angle `alpha` from a cliff of height H above the sea level. If it falls into the sea at a distance D from the base of the cliff, show that its maximum height above the sea level is
`[H+(D^(2) tan^(2) alpha)/(4(H+D tan alpha))]`

Explanation

To solve the problem, we need to find the maximum height of a projectile launched from a cliff of height \( H \) at an angle \( \alpha \) above the horizontal, which lands at a distance \( D \) from the base of the cliff.

### Step-by-step Solution:

1. **Identify the Components of Motion**:
- The initial velocity \( u \) can be resolved into horizontal and vertical components:
\[
u_x = u \cos \alpha \quad \text{(horizontal component)}
...