1. The Classical Projectile Height Function

1. The Classical Projectile Height Function

From Newton's second law of motion ($F = m a = -m g$), the instantaneous altitude $h(t)$ at time $t$ is: $h(t) = -\frac{1}{2} g t^2 + v_0 t + h_0$

where:

• $g = \text{effective gravitational acceleration}$ (in metric units, $-\frac{1}{2}g \approx -4.9 \text{ to } -5 \text{ m/s}^2$)
• $v_0 = \text{initial upward vertical launch velocity (m/s)}$
• $h_0 = \text{initial launchpad elevation above ground (m)}$
• $t = \text{time elapsed since liftoff (s)}$