Equations for detecting collision

[kachilous]

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.

 

[DickL]

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.

 

[kachilous]

What do you mean by time step analysis?

 

[DickL]

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.

 

[PJC01]

Great job on creating a program that simulates an object being thrown off a building! To implement collision detection, you will need to use the equations of motion to calculate the object's velocity and position at impact. These equations are:

- Velocity at impact (vf) = initial velocity (vi) + acceleration (a) * time of impact (t)
- Position at impact (xf) = initial position (xi) + initial velocity (vi) * time of impact (t) + 1/2 * acceleration (a) * (time of impact (t))^2

In your case, the initial position would be 50 m (since the object is being thrown off a 50 m building), and the initial velocity would be the initial velocity of the object at the time of throwing. The acceleration in this case would be due to gravity, which is -9.8 m/s^2.

You are correct in using the time of collision equation to find the time of impact. Once you have the time of impact, you can plug it into the equations of motion to find the object's velocity and position at impact.

In order to factor in the coefficient of restitution, you will need to use the following equation:

- Final velocity after impact (vf') = coefficient of restitution (e) * initial velocity (vi)

You can then use this final velocity to calculate the object's new position using the equation for position at impact mentioned above.

I hope this helps you with your project. Keep up the good work! As a scientist, it's important to always refresh and apply your knowledge of Physics. Good luck!