What are the correct heights for Tom after a collision with Dan in a halfpipe?

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SUMMARY

The discussion focuses on the heights Tom reaches after colliding with Dan in a semicircular halfpipe, considering two types of collisions: totally inelastic and elastic. For the inelastic collision, both Dan and Tom reach a height of h/4. However, the calculations for the elastic collision are incorrect, as the expected height for Tom needs further analysis beyond the provided equations. The key equation used is H = v² / 2g, which is essential for determining the heights post-collision.

PREREQUISITES
  • Understanding of basic physics concepts, particularly conservation of momentum.
  • Familiarity with kinematic equations, specifically H = v² / 2g.
  • Knowledge of collision types: elastic and inelastic collisions.
  • Basic principles of energy conservation in mechanical systems.
NEXT STEPS
  • Review the principles of conservation of momentum in elastic collisions.
  • Study the differences between elastic and inelastic collisions in detail.
  • Learn how to derive final velocities post-collision using momentum equations.
  • Explore the implications of energy conservation in skateboarding dynamics.
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Physics students, educators, and anyone interested in understanding collision mechanics and energy transfer in sports dynamics.

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Homework Statement


Dan and Tom are skateboarding in a large semicircular halfpipe. Dan starts out from rest at a height h and collides with Tom standing at the bottom. Dan and Tom have about the same mass. After the collision, which height will Tom reach? Let's neglect friction and consider the following two extreme cases:
a) The collision is totally inelastic.
b) The collision is elastic. [/B]

Homework Equations



H = v² / 2g

The Attempt at a Solution


For part a) = V²/4 / 2g leaves them at h/4
For part b) = v^2/4/2g leaves them at h/4

Part a is correct but part b isn't. Any help would be appreciated[/B]
 
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