Radius of a projectile at the top of its path.

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SUMMARY

The discussion focuses on calculating the radius of curvature of a projectile's parabolic motion at the apex of its trajectory. The radius of curvature is defined as the radius of the circle that locally matches the projectile's path. The problem also explores determining the launch angle that results in the radius of curvature being half of the maximum height achieved by the projectile. Key concepts include projectile motion, parametric curves, and centripetal acceleration.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with parametric equations in calculus
  • Knowledge of centripetal acceleration
  • Ability to calculate maximum height of a projectile
NEXT STEPS
  • Study the derivation of the radius of curvature for parametric curves
  • Learn how to calculate maximum height in projectile motion
  • Explore the relationship between launch angle and projectile trajectory
  • Investigate centripetal acceleration in the context of projectile motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators looking for problem-solving strategies in kinematics.

CornMuffin
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Homework Statement


A projectile is fired at spead v0 and angle [tex]\Theta[/tex]. What is the radius of curvature of the parabolic motion
a) at the top?
b) At what angle should the projectile be fired so that the radius of curvature at the top equals half the maximum height?

(the projectile is fired on a horizontal plane)

Homework Equations


Radius of curvature is defined to be the radius of the circle that matches up with the path locally at a given point.


The Attempt at a Solution




I just need help getting started with this problem I'm sure I can finish it on my own, I'm just not sure how to find the radius of curvature on a parametric curve. I probably can do part b on my own after I figure out how to do part a.
 
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What's the centripetal acceleration at the top? (Hint: There is no vertical speed at the top).
 

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