Swinging Over the Water Hole

Abstract

A child takes a running start, grabs hold of the free-hanging end of a rope at the edge of a water hole at x = 0, swings upward, and lets go of the rope at some point, flying freely through the air until he lands in the water at x = R . For small initial speeds, the maximum range R is obtained by releasing the rope just short of its turning point and dropping almost straight down into the water from rest. On the other hand, as a child's running speed gets larger and larger (compared to the square root of the product of the length of the rope and earth's gravitational field), the rope should be released at an angle of about pie / 4 to maximize the range. That is, the optimum trajectory of a child is dominated by pendulum motion at low running speeds and by projectile motion at high initial speeds.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2011
Accession Number
ADA551200

Entities

People

  • Carl E. Mungan
  • Trevor C. Lipscombe

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Case Studies
  • Electronic Mail
  • Energy
  • Gravitational Fields
  • Information Operations
  • Kinetic Energy
  • Pendulums
  • Physics
  • Potential Energy
  • Projectiles
  • Students
  • Trajectories
  • United States Naval Academy

Readers

  • Aerodynamics/Aeronautics.
  • Educational Psychology
  • Electrical Engineering