Why Velocity Equals Zero at Maximum Height: Calculus of Projectile Motion

Описание: A firework launches at 256 feet per second. When should the fuse trigger the explosion for maximum height? This video walks through the calculus of projectile motion, showing how derivatives reveal the exact moment when a projectile stops rising and begins falling—the instant when velocity equals zero.

Key concepts covered:
• The physical meaning of each term in the height function h(t) = 256t - 16t²
• Using the power rule to derive the velocity function h'(t) = 256 - 32t
• Setting the derivative equal to zero to find critical points
• Interpreting positive and negative velocity as upward and downward motion
• Why maximum height occurs where velocity (not acceleration) equals zero
• The relationship between parabolic height curves and linear velocity functions
• Applying optimization principles beyond physics problems

ORIGINAL SOURCE
This video distills concepts from:    • Calculus 1 Lecture 2.4:  Applications of t...  
Full credit to the original creator for the educational content.

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