Projectile motion question totally stuck

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Homework Help Overview

The discussion revolves around a projectile motion problem involving a cannon firing projectiles up a hill at an angle. The goal is to determine the optimal angle for maximum range along the hill's slope, which is defined by an elevation angle alpha.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss separating the initial velocity into horizontal and vertical components and applying relevant equations for projectile motion. There are attempts to model the hill's slope and questions about treating it as a flat surface versus incorporating its angle. Some participants express confusion about the relationship between the projectile's trajectory and the hill's angle.

Discussion Status

Participants are actively engaging with the problem, sharing their attempts and reasoning. Some have suggested methods for deriving equations, while others are exploring the implications of the hill's angle on the projectile's motion. There is a collaborative effort to clarify misunderstandings and refine approaches, but no consensus has been reached on a specific solution.

Contextual Notes

There are indications of confusion regarding the application of projectile motion equations in the context of a sloped surface, as well as varying interpretations of how to incorporate the hill's angle into calculations. Participants are also grappling with the complexity of the resulting equations and the presence of multiple unknowns.

  • #61
Thanks! I haven't seen that trig identity for years. It sure is handy in this problem.

emyt, if you are still watching, he has used
sin(x+y) + sin(x-y) = 2sin(x)cos(y)
You probably did it in high school using
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
and the same with y replaced by -y. These last identities are the commonly used "addition and subtraction formulas".
 

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