postion vetcors question..:(?

Question

...at time t=0 John (J) is at 40j...and Norma (N) is at 20i...
John has a constant velocity of 5ms-1 and Norma is going at (3i+4j)ms-1...show that they will collide..and at what time...

*how does one find the time (of collision possibly) in any position vectors question... ..?is there a specific equation...i think -position vector+initial r + (v*t) is right...but with the i and j's i get confused..:S
please help

i and j represent the x and y axis.

john moves at 5i m/s

Answer 1

What do the i and j represent ? coordinates in a rectangular grid ? in that case you already know that Normas speed is also 5 m/s, however she moves more or less diagonally and John moves along a straight line.

Does John move 5i m/s or 5 j m/s ?
OK if John is at 40 j and moves with 5i m/s, and Norma starts at 0j and 20i, after 10 seconds Norma will be at 50i and 40j. And John will be at 50 i and 40 j. There is your collision.

Generally you find the time by dividing the difference of either coordinate (distance) by the speed in either direction (distance / time) which gives you time. In this case, 40 / 4 = 10.

Answer 2

To go further you need to state John´s vector velocity as you don´t give direction
Norma´s position is 20i +(3i+4j)t
John´s position is 40j+(a i+b j) t
(20+3t)i+4j t = at i+(40+bt)j
20+3t=a
4=40+bt
There must be a common value of t