Projectile Motion with Air Resistance problem

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SUMMARY

The discussion centers on determining the optimal launch angle for a projectile with air resistance, specifically questioning the assertion that the angle for maximum range is 53 degrees. Participants clarify that, traditionally, the optimal angle without air resistance is 45 degrees. However, they assert that with air resistance, the optimal angle is typically lower than 45 degrees, depending on the specific formula used for air resistance, which can be linear or quadratic. The complexity of the equations governing projectile motion with air resistance necessitates numerical solutions, as no general solution exists.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with projectile motion concepts
  • Knowledge of air resistance models (linear and quadratic)
  • Basic differential equations and numerical methods
NEXT STEPS
  • Study the derivation of projectile motion equations with air resistance
  • Learn about numerical methods for solving differential equations
  • Explore the differences between linear and quadratic air resistance models
  • Investigate the impact of varying launch angles on projectile range
USEFUL FOR

Students studying physics, educators teaching projectile motion, and anyone interested in the effects of air resistance on projectile trajectories.

ahadpoolghaha
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hi.
Suppose that a projectile of mass "m" is launched, from ground level in a horizontal plain, making an angle teta to the horizontal .(with air resistance).now in which angle "m" has the maximum range? .(our teacher said that we should find 53 degrees for teta).please prove it.
(first of all we should find (x-t) and (v-t) equations.then we should find the equation of range with those 2 equations and then we should derivative the rang equation(dr/d(teta).
so we will find the angle in which the mass "m" has the maximum range.this is my idia.if anyone knows the answer of this question,please tell it.i need the diagram of the motion too.)thanks a lot.:smile:
 
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I think this thread should be in the homework location... none the less you state with air resistance. My understanding is that the equation that describes air resistance is pretty complicated and is normally simplified to either linear or quadratic approximation. But Newtons laws of motion with quadratic drag in horizontal and vertical motion results in a pair of differential equations that can only be solved numerically (there is no general solution).
 
Welcome to PF!

ahadpoolghaha said:
… our teacher said that we should find 53 degrees for theta …

Hi ahadpoolghaha! Welcome to PF! :smile:

(I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? :smile:
 
tiny-tim said:
Hi ahadpoolghaha! Welcome to PF! :smile:

(I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? :smile:

I'm pretty sure that theta is always lower than 45 degrees with any plausible
formula for air resistance (linear, quadratic)
 

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