Prove that two ships collide

Daniel123 · 2007-09-21 03:12:22

Basically I have a mechanics question, and I have got down to the part where I must prove that the position vectors are equal (as the two ships collide), for an unknown time t.

I have written (which I know to be correct):

i(7t) + j(600 + 8t) = i(7t) + j(120 + 24t)

The way I would normally do it is by equating the 'i's with the 'i's and the 'j's with the 'j's, and then finding the value for t in both, to show that t is equal for both, therefore they collide.

However, if I equate 7t and 7t, then I can't do anything there, except show that the 'i' coordinate for both ships is the same. If I then equate the 'j's, I get down to a time of 30s, but that doesn't necessarily prove that the 'j' coordinate is equal for both ships, does it?

If not, is there a way of doing it?

thanks.

JaneFairfax · 2007-09-21 03:19:34

Daniel123 wrote:

If I then equate the 'j's, I get down to a time of 30s, but that doesn't necessarily prove that the 'j' coordinate is equal for both ships, does it?

Yes, it does. At t = 30, both ships will collide at the point (210,840).

mathsyperson · 2007-09-21 03:20:48

That is the way to do it, you're just getting confused by the i's.

Equating the j's gets you 600 + 8t = 120 + 24t, and as you said, they're equal when t=30.

Equating the i's just gives 7t = 7t. This is true no matter what t is, which of course means that it's true when t=30.

Therefore, both ship's coordinates will be equal (210,840) at t=30 and so they will collide.

---
Edit: Grr, Jane beat me again.

To make this post useful though, there is another "lazier" way you can do it.
The question doesn't want to know when or where the ships collide, it just wants proof that they will.

That means that you can equate the i's and see that the i coordinate will be true for all t, and then deduce that they will crash as long as there is a t when the j's are equal.

Looking at the j's equation, you can see that the ships are moving in the same direction and the one with the lower initial position is moving faster. Therefore, the j's will coincide at some point and so the ships will collide. And all without doing any actual maths!

Daniel123 · 2007-09-21 03:37:14

Haha interesting method.. but the next part of the question actually said find the time when they will collide, and the position vector of collision.

Thanks!

bossk171 · 2007-09-21 04:52:49

I'm a little confused... are i and j axis like x and y in the Cartesian plane? If so, why use i and j and not x and y.

When I took physics we used x and y. Is this because it was a high school physics class and you're in college? Or is it because I'm American? Or just because?

mathsyperson · 2007-09-21 05:23:57

There's no reason, really. i and j are just "traditionally" associated with perpendicular vectors like that.

Daniel123 · 2007-09-21 05:26:13

Well, I'm in 'sixth form', which I think is the equivalent of high school. My year is for 16-17 year olds, anyway.

Basically, i,j notation is used to avoid confusion with actual x,y coordinates. For example, the numbers (3,4) represent a set of coordinates, but the expression 3i + 4j represent a vector. i is representative of the movement along the x axis, and j along the y axis. I dont see the point really.. it confuses things for me... i and j look too similar when written!

Last edited by Daniel123 (2007-09-21 05:26:56)

bossk171 · 2007-09-21 05:38:16

Maybe the reason I haven't seen this before is because I've had minimal experience with vectors. In our class we would simply define a coordinate system and work with x and y. I know what a vector is use, but really didn't use them.

Thanks for clearing that up.

Math Is Fun Forum

#1 2007-09-21 03:12:22

Prove that two ships collide

#2 2007-09-21 03:19:34

Re: Prove that two ships collide

#3 2007-09-21 03:20:48

Re: Prove that two ships collide

#4 2007-09-21 03:37:14

Re: Prove that two ships collide

#5 2007-09-21 04:52:49

Re: Prove that two ships collide

#6 2007-09-21 05:23:57

Re: Prove that two ships collide

#7 2007-09-21 05:26:13

Re: Prove that two ships collide

#8 2007-09-21 05:38:16

Re: Prove that two ships collide

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