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Cyberpunk Math Lab: The Non-Linear World FREE
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Quadratic Applications
Learning Objectives
- Model projectile motion
- Find maximum height
- Determine time of flight
Key Concepts
Projectile Motion
h(t) = -16t² + v₀t + h₀ (feet) or -4.9t² + v₀t + h₀ (meters)
Maximum Height
Occurs at vertex: t = -b/(2a)
Theory
**Projectile equation:** h(t) = -16t² + v₀t + h₀
- v₀ = initial velocity (ft/s)
- h₀ = initial height (ft)
- Maximum at t = -v₀/(2×(-16)) = v₀/32
**Key points:**
- Launch: t = 0, h = h₀
- Max height: t = v₀/32
- Landing: h(t) = 0 (solve quadratic)
Examples
h(t) = -16t² + 64t. Max height?
Solution: t = 64/32 = 2s. h(2) = -64 + 128 = 64ft