# Thread: Hard vectors help - intersection, time etc.

1. ## Hard vectors help - intersection, time etc.

So there are three ships, which have position vectors, r and velocity vectors v, at 7.00am one morning:

FF: (i and j are unit vectors parallel to x and y axis respectively)
r = 186i + 44j
v = 8i + 12j

WS:
r = 228i + 58j
v = -16i + 4j

HW:
r = 215i + 101j
v = -12i -16j

a) Prove that FF and WS, continuing with their stated velocities, will collide.
I let both v vectors equal each other to get 6i and 6j, but I really don't think that is correct.

b) Time of collision and position vector of its location.

c) At the moment of impact between FF and WS, HW changes directions and heads to the collision at 1.5x its previous speed. How many minutes after the collision does HW arrive at the scene?

All help would be appreciated

2. ## Re: Hard vectors help - intersection, time etc.

a) The location of FF after a time t is (186+8t)i + (44+12t)j.
Hint. If they collide then their i and j positions will be the same at the same time.

b) Add the time you found in a) onto 7:00am

c) Find the position of HW when the collision takes place. Find the distance between HW and the crash. the new speed of HW is 1.5 times the *Magnitude* of the old speed. You now know the distance it has to go and the speed it is going at so you can find when it arrives.