Will 2 particles with paths crossed collide?

[jefer]

Homework Statement

The first particle A is starting at origin and it has a velocity vector with magnitude 10km/h and moves at an angle of 30 degrees relative to y axis. The second particle B is starting at (0,5) and it has velocity vector with magnitude 8km/h and moves at an agle of 60 degrees relative to y axis. Will these 2 particles colide, and if not, what is the minimal distance they will be at?

Homework Equations

The Attempt at a Solution

I found the velocity vectors with given angles/magnitudes. I'm not sure what to do now.

 

[azizlwl]

The particles will collide at time where both at x and y displacement are equal if time t exist.

 

[jefer]

Yeah I got position vector r_A and r_B from formula r(t)=v*t, where r and v are vectors. They have this form r_A=x*t*i + y*t*j where i and j are unit vectors. What do I get from equatting positions, how do I calculate time from that?

The correct answer is that they don't collide and minimal distance is 1.8km. So does it really make sense to equate postitions if we're not 100% sure they'll collide? I am really confused :/

 

[azizlwl]

Find time in y direction where both displacements are equal. Then on x direction or component. If both time are equal then they meet.

 

[TSny]

jefer,

Have you studied the concept of relative velocity? If so, what is the velocity of B relative to A?

 

[vela]

So does it really make sense to equate positions if we're not 100% sure they'll collide? I'm really confused. :/

When trying to solve the problem, you can assume they'll collide and see what consequences arise from that assumption. If the consequences don't make sense, then you can conclude that the assumption was wrong. It's like a proof by contradiction in math, if you're familiar with those.