Point of intersection (collision)

[Mosab Ahmed]

Hello ;

I need to find the formula to find the point of intersection (x,y) of two moving objects.

if we know there current location and the distance between them , and the velocity for each of them as illustrated in the picture.

- I believe the formula has to consider the angle ( theta)

How to find the point of collision between two moving objects in 2d plane .. if we know :

- the current position of both object
Object1 in ( a1,b1)
Object2 in (a2,b2)
the velocity for both object
The distance between them

 

[Dr.Peterson]

I need to find the formula to find the point of intersection (x,y) of two moving objects.

if we know there current location and the distance between them , and the velocity for each of them as illustrated in the picture.

- I believe the formula has to consider the angle ( theta)View attachment 23328

How to find the point of collision between two moving objects in 2d plane .. if we know :

- the current position of both object
Object1 in ( a1,b1)
Object2 in (a2,b2)
the velocity for both object
The distance between them

You'll actually need the direction between them, not just the distance. That is perhaps the reason for the angle [MATH]\alpha[/MATH] (alpha) shown, which is perhaps what you mean by "theta".

But I hope you realize they will not collide unless they happen to arrive at the same point at the same time, which will not typically be true. You may need to also specify how close counts as a collision -- that is, allow for some limited error.

I'm also a little unhappy with the notation in the image, which looks as if you had a cross (vector) product between time (a scalar) and v_t (a vector), which is of course wrong.

What have you tried to solve the problem? We'd like to at least see what sort of methods you have in mind, in order to know what to suggest.

 

[skeeter]

let the target start at the origin of the Cartesian plane, (0,0), with velocity along the x-axis, [math]v_t \hat{i}[/math].

the chaser starts at coordinates, [MATH](d\cos{\alpha}, d\sin{\alpha})[/MATH] and moves with velocity, [MATH]v_c\hat{i} + v_c \hat{j}[/MATH].

equations for intersection at time [MATH]t[/MATH]...

[MATH]d\cos{\alpha} + v_c \hat{i} \cdot t = v_t \hat{i} \cdot t[/MATH]
[MATH]d\sin{\alpha} + v_c \hat{j} \cdot t = 0[/MATH]