Mechanics Thing(algebra craziness)

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SUMMARY

The discussion focuses on consolidating three equations to calculate the distance a projectile travels when launched at an angle from a height above ground. The relevant equations include V = √(2gh), Dy = 0.5 * a * t², and Dx = vx * t. The challenge lies in simplifying complex expressions that arise during the consolidation process, such as v⁴ * cos²(θ) * sin(θ). The user seeks assistance in achieving a more manageable formula for projectile motion from a non-zero height.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Knowledge of conservation of energy concepts
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research how to derive projectile motion equations from conservation of energy
  • Learn about the effects of initial height on projectile trajectories
  • Study advanced algebra techniques for simplifying complex expressions
  • Explore the use of simulation tools for projectile motion analysis
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in experimental mechanics or projectile motion analysis.

naes213
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Homework Statement


The task is to consolidate the three equations used to calculate the distance that a projectile fired at an angle and at a height above the ground will travel. Its an experiment with an adjustable projectile launcher. Calculate the velocity using conservation of energy based on the height straight up that the projectile reaches.


Homework Equations



V=rad(2gh), Dy=.5*a*t^2, Dx=vx*t

The Attempt at a Solution



All attempts at consolidating this into one step have result in enormous ridiculous fractions that are very difficult to simplify. Things like v^4*cos^2(theta)*sin(theta) and large radical expressions. Any help wpuld be greatly appreciated!
 
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You might want to read up here: http://www.pa.uky.edu/~moshe/phy231/lecture_notes/projectile.html

Basically you're just trying to do the same thing except for a certain starting height which isn't 0.
 
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Thanks!
 

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