Finding the optimal launch for a projectile?

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SUMMARY

The discussion focuses on deriving the optimal launch angle for a projectile, specifically a water balloon launched from a height H with an initial velocity Vo, while neglecting air resistance. The user aims to utilize Newton's Second Law and kinematic equations to establish a formula for maximum horizontal distance (xmax) and subsequently determine the optimal angle (theta) for achieving this distance. The user encountered an error in their calculations, incorrectly concluding that the optimal angle was 89 degrees, and seeks assistance in correcting this through MATLAB's fzero function.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with kinematic equations for projectile motion
  • Basic knowledge of MATLAB programming, specifically the fzero function
  • Concept of trajectory optimization in physics
NEXT STEPS
  • Study the derivation of projectile motion equations, focusing on maximum range calculations
  • Learn how to implement MATLAB's fzero function for root finding
  • Research the effects of launch angle on projectile distance in physics
  • Explore advanced kinematic simulations to visualize projectile trajectories
USEFUL FOR

Physics students, engineers, and anyone interested in optimizing projectile motion calculations and simulations using MATLAB.

Boatman(J)
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Suppose I wanted to launch a water balloon off a cliff of a known height of H and known initial Velocity of Vo, where we can neglect air resistance. Using Newton's Second Law and differentiating it, how can i derive an equation for maximum distance traveled (xmax) at an angle theta? Then from the equation derived for xmax, how can I create another equation that can be use to derive the optimal angle which allows the balloon to travel the xmax? I will then use that equation for the optimal angle to find the optimal angle by root finding with the use of fzero in matlab.

I did this through kinematics but it was done wrong and kept telling me that optimal angle was 89 degress.

Can someone please help?
 
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