How Do Particles P and Q Collide in Vector Terms?

[jdklek]

Hi guys, I'm reallyyyy stuck on this so I would really appreciate your help, cheers :)




2. Particle P passes through posiion A (12,3) with constant velocity i + 2j m/s. At the same time Particle Q passes through position B (3,-3) with c.v 2.5i + 3j m/s. Find the position vectors of P and Q after time t seconds. Show that they collide. If the point of collision is X, find the time taken for P to travel from A to X. Find the position vector of X.



3. It's just finding the position vector of X that I need help with...please?! :D
Thankyouu!
x

 

[Doc Al]

What have you done so far?

 

[HallsofIvy]

Have you found the position vectors (as functions of t) for P and Q to begin with?

 

[Andrew Mason]

Hi guys, I'm reallyyyy stuck on this so I would really appreciate your help, cheers :)




2. Particle P passes through posiion A (12,3) with constant velocity i + 2j m/s. At the same time Particle Q passes through position B (3,-3) with c.v 2.5i + 3j m/s. Find the position vectors of P and Q after time t seconds. Show that they collide. If the point of collision is X, find the time taken for P to travel from A to X. Find the position vector of X.

i and j are the orthogonal unit vectors in the plane:

$$\vec {v_P} = 1\hat i + 2\hat j \text{ m/sec}$$

and

$$\vec {v_Q} = 2.5\hat i + 3\hat j \text{ m/sec}$$

Write out the displacement of P from the origin as a function of time: $d_P(x(t), y(t))$ and do the same for Q.

What is the relationship between the displacements (ie the coordinates) of P and Q at the time of a collision?

AM