Angle of projection for maximum range

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SUMMARY

The angle of projection for maximum range on an inclined plane is determined by the formulas (π/4 - β/2) for an upward projection and (π/4 + β/2) for a downward projection. These formulas account for the angle of inclination (β) and are derived from the principles of projectile motion. When dealing with a flat ground, the method remains consistent, requiring the range (R) and the initial velocity angle to optimize the projectile's trajectory. Understanding differentiation is essential for deriving these maximum range angles effectively.

PREREQUISITES
  • Basic understanding of projectile motion principles
  • Familiarity with angles and trigonometric functions
  • Knowledge of differentiation in calculus
  • Concept of range (R) in projectile motion
NEXT STEPS
  • Study the derivation of projectile motion equations
  • Learn about the impact of angle of inclination on projectile trajectories
  • Explore differentiation techniques for optimizing functions
  • Investigate the effects of initial velocity on range calculations
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Physics students, educators, and anyone interested in understanding projectile motion and optimization techniques in mechanics.

Abhishek332211
20171006_175217.png
Hi,
I can't seem to work out how angle of projection for maximum range comes out to be (pi/4 - Beta/2)

This happens when the projectile is protected up the inclined plane.

Similarly, I couldn't understand how the angle comes out to be (pi/4 + Beta/2) when the projectile is protected down the inclined plane.

And the other two formulas that have been marked off.

Thanks in advance
 
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When the projectile is shot onto a flat ground, do you know how to find the angle for maximum range?

The method is identical here. You are given "R", the range of the projectile. Only this time, you are dealing with two angles, the angle for the initial velocity, and the angle of the inclined plane. For a fix angle of the inclined plane, how would you use "R" to find maximum "R" with respect to the projectile initial angle?

Zz.
 
Have you studied differentiation yet?
 

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