Equations for detecting collision

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Discussion Overview

The discussion revolves around implementing collision detection in a simulation of an object being thrown from a height of 50 meters. Participants explore the necessary equations and concepts related to collision dynamics, including the object's velocity, position at impact, and the coefficient of restitution.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant proposes a formula for calculating the time of impact based on the object's initial velocity and acceleration due to gravity.
  • Another participant emphasizes the need to determine the object's position when it reaches ground level (y=0) to confirm a collision has occurred.
  • A later reply introduces the concept of time step analysis, explaining that it involves using constant time increments to compute position, velocity, and acceleration iteratively.
  • Participants discuss the importance of calculating the object's velocity and position at the moment of impact for further analysis of post-collision dynamics.
  • One participant mentions the coefficient of restitution, suggesting it will need to be factored into the collision calculations.

Areas of Agreement / Disagreement

Participants generally agree on the need to calculate the position and velocity at impact, as well as the relevance of the coefficient of restitution. However, the discussion on time step analysis introduces a different approach that has not been fully explored or agreed upon.

Contextual Notes

There are unresolved aspects regarding the specific equations needed for collision detection and the implications of using time step analysis versus other methods. The discussion does not clarify the assumptions behind the proposed equations or the conditions under which they apply.

Who May Find This Useful

Individuals interested in programming simulations, physics students looking to understand collision dynamics, and those exploring numerical methods for solving physics problems may find this discussion relevant.

kachilous
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I have created a program that simulates an object being thrown off a 50 m building.
Now I would like to implement collision detection. What equations would I need to accomplish this? I am taking Physics right now, so my Physics is a little rusty.

I know I will have to find the time of collision:
timeImpact = (-vy - sqrt((vy*vy) - (2*ay*y)) / (2*.5*ay))

Will I also have to find the object's velocity and position at impact too?

I also decided that the object's coefficient of restitution will be .5.
So I know I will have to factor that in as well.

Any help would be appreciated.
 
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You will need the position (y) of the object. When the position of the object is equal to the altitude of the ground (y=0) its collided. In order to analyze the post collision dynamics you will probably also want the time and velocity. If your approach is a time step analysis, it is quite easy to also compute the time, position, velocity, acceleration in a time step table format.
 
What do you mean by time step analysis?
 
A time step analysis uses a constant increment of time, say 0.1 sec, and computes the necessary data (total time, position, velocity, acceleration) for each step in time. Then uses those results to compute the next increment.
 

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