Phase 1: Data Assimilation.
- Initial velocity: \( u = 20 \, \text{m/s} \)
- Terminal velocity at apex: \( v = 0 \, \text{m/s} \)
- Gravitational acceleration: \( g = 9.8 \, \text{m/s}^2 \) (vectorially \( a = -9.8 \, \text{m/s}^2 \))
Phase 2: Kinematic Equation Application.
Employing the second kinematic equation, which links initial velocity, terminal velocity, acceleration, and vertical displacement (maximum altitude):
\[v^2 = u^2 + 2a s\]
Inputting the established parameters:
\[0 = (20)^2 + 2 \times (-9.8) \times s\]
\[0 = 400 - 19.6s\]
\[19.6s = 400\]
\[s = \frac{400}{19.6} \approx 20.4 \, \text{m}\]
Conclusion: The maximum altitude attained by the projectile is approximately \( 20.4 \, \text{m} \).