Collision between two moving objects (one with a non-known trajectory)?

In summary, The conversation discusses a solution for finding the collision point between two objects, A and B, using math and the law of sines. The solution involves finding the distance between the objects, dividing it by B's speed, and repeating the process until a precise answer is obtained. The use of the law of sines simplifies the problem into finding the intersection of two lines. The relevance of AB/t in a real-world context is also considered.
  • #1
Iximeow
2
0
Alright, I've been working on this on my spare time for the past few weeks, and have a solution that ~works~, but I'm not happy with at all.

The general idea is to have two objects, A and B, where A's velocity and position are known, B's position and speed are known, but the direction B travels in can vary. I want to find where and when the two objects will collide, before even considering if it can happen at all.

Going to type out my math as it's simpler than just explaining it all in Engrish.

Ax, Bx = A's x-position, B's x-position
Ay, By = similarly, A's y-position, B's y-position
Avx, Avy = A's x-velocity, y-velocity

||B|| = B's speed

My solution thus far has been to find the distance from B to A, D1: sqrt({Bx-Ax}^2+{By-Ay}^2)

Then taking ||B||, and dividing D1 by it, giving T1 = D1/||B||

Then finding the distance from B to A(T1), D2: sqrt({Bx-Ax-Avx*T1}^2+{By-Ay-Avy*T1}^2)

Again, distance divided by ||B||, gives a better distance to correct for: T2 = D2/||B||

Then finding D3: sqrt({Bx-Ax-Avx*T2}^2+{By-Ay-Avy*T2}^2)

etc etc continuing on until Tn gets sufficiently small that I don't need to get closer, then having Tn and A(Tn), knowing that A(Tn) is close enough to the collision point I'm looking for. Initially, before I did the math, I was hoping to get something that I could use a limit for as n -> infinity, and get a precise answer, but from the way the math expands.. I'm pretty sure I can't do that?

If anyone knows what I may or may not be doing wrong, or a better way of finding this, I'd love you forever? :D
 
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  • #2
... Don't mind me; reworking an idea I had a while back to use the law of sines gave a good answer.

Setting up a triangle with A and B's position as vertices, the collision point C as the third vertex, then knowing that AC = Bv*t, BC = Av*t, and easily finding the angle by A, and using the law of sines to know sin(A)/(Bv*t) = sin(B)/(Av*t). The t drops out, and then the angle by B is simple to find, which makes the problem into finding the intersection of two lines, and a bit more simple math to find how long it takes for one of the two objects to get to C.

Yay, precise answers. Now just wondering if AB/t has any real-world meaning or use.. hmm...
 

1. What factors determine the outcome of a collision between two objects?

The outcome of a collision between two objects is determined by several factors, including the mass, velocity, and angle of collision of each object, as well as the elasticity and shape of the objects involved.

2. How can we predict the trajectory of an object after a collision?

In order to predict the trajectory of an object after a collision, we must first have information about the initial velocities and angles of the objects involved, as well as their masses and the forces acting on them during the collision. Using this information, we can apply principles of physics, such as conservation of momentum and energy, to calculate the final trajectory of the objects.

3. Can a collision between two objects result in a perfectly elastic outcome?

Yes, a perfectly elastic collision can occur when the kinetic energy of the objects before the collision is equal to the kinetic energy after the collision. This means that the objects will bounce off each other without any loss of energy. However, in real-world situations, there is always some energy lost due to factors such as friction and deformation of the objects involved.

4. How does the angle of collision affect the outcome of a collision?

The angle of collision can greatly affect the outcome of a collision. If the objects collide head-on, the forces acting on them will be much greater than if they collide at an angle. This can result in more energy being transferred between the objects, potentially causing more damage or a greater change in trajectory.

5. What role does the coefficient of restitution play in a collision?

The coefficient of restitution is a measure of an object's elasticity and determines how much of its kinetic energy is retained after a collision. A higher coefficient of restitution means that more energy is retained, resulting in a more elastic collision. This can affect the final trajectory of the objects and the amount of damage that occurs during the collision.

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