What is the solution to finding the time when two objects collide in 2d space?

[adoado]

Hello all ^^

I have two objects moving in 2d space, their positions given by:

x₁ = r₁*cos(s₁ * time)
y₁ = r₁*sin(s₁ * time)

and

x₂ = r₂*cos(s₂ * time)
y₂ = r₂*sin(s₂ * time)

Essentially, I want to see if they collide or exist in the same place at any time. So I am guessing I need to solve twice for both x and y collisions.

I did this, but am stuck isolating time (or solving the problem :P)...

r₁*cos(s₁ * time) = r₂*cos(s₂ * time)

I am trying to isolate the time they collide (if they do)...

I am not too good at maths, and the answer is probably really simple, but any help is greatly appreciated! This is not homework, its for a hobby computer game I am trying to make.

Cheers,
Adrian

 

[tiny-tim]

I have two objects moving in 2d space, their positions given by:

x₁ = r₁*cos(s₁ * time)
y₁ = r₁*sin(s₁ * time)

and

x₂ = r₂*cos(s₂ * time)
y₂ = r₂*sin(s₂ * time)

Essentially, I want to see if they collide or exist in the same place at any time.

Hello Adrian!

These are circles, with radius r₁ and r₂, respectively, and both centred at the origin (0,0).

So the objects won't collide unless r₁ = r₂