# SUM1 tell me wat i am doing WRONG

1. Sep 20, 2006

### ku1005

PLZ SUM1 tell me wat i am doing WRONG!!

the follwing Q is really annoying me....because i cant work out where i am goin wrong arrgghhhhh

At time t= 0 seconds particles A and B are moving with velocities (-10i-2j)m/s and (-2i-6j)m/s respectively, the postion vector of B relative to A being (-16i+13j)m. Assuming A and B maintain these velocities find the least distance of seperation bewteen the 2 particles in the subsequent motion and the value of t for which it occurs.

(PS...we have to use the scalar product method....and yes i can do it with calculus methods....but im really annoyed i can tget this)

here is my working:

A v B = va-vb = (-8i+4j) - (ie consider situation as "B" being staionary and "A" moving)

B r A (or vector AB)= -16i-13j (ie we are told this)

Vector PB = Vector AB - Vector AP
=(-16i-13j)-t(-8i+4j)
=(-16+8t)i +(-13-4t)j

Given Vector PB will be perpendicular to (-8i+4j) therfore the scalar product of the 2 will = 0

such that : -8(-16+8t)+4(-13-4t) = 0

therfore i get t = 0.95......WHICH IS INCORRECT, the answer is 2.25.....can anyone see my ERROE....i really appreciate this!!!!

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2. Sep 20, 2006

### HallsofIvy

Staff Emeritus
Why "- Vector AP"? If AP is the velocity vector of A relative to B and AB the position vector of A relative to B at time t= 0, then the position vector of A relative to B is AB+ APt.

I don't follow this. The motion of A relative to B, vector PB, is a straight line. It will not be perpendicular to the initial position vector- that's irrelevant. Instead, minimize the length of vector PB.

3. Sep 20, 2006

### ku1005

yes i understand that you can simply minimise vector PB....however our topic atm is the scalar product, and it is stipulated that we must use this to answer the question.

“Vector PB = Vector AB - Vector AP” since if you add them as the way u said, it in no way gives vector PB (ie P to B) I agree yes AB+ APt. = however, do u not agree that AP must be in he opposite direction to give the required vector AB….i just skipped this step and inserted the “-“ stright away….

I could hav done ur method and said:

AB+ APt = vector of A relative to B = (-16i+13j)+ -t(-8i+4j)

If u draw it it makes sense since, since isn’t “A relative to B” = vector BA????? This is why, again if you draw it, vector BA= (Position vector) A – (position vector) B.

As for the following “I don't follow this. The motion of A relative to B, vector PB, is a straight line. It will not be perpendicular to the initial position vector”

The point at which these 2 particles are closest, given they don’t collide, is the point at which PB is perpendicular to the position vector of t(AvB), ie relative to time hence the line t(-8i+8j), I am not saying it is perpendicular to the initial position vector, I am trying to say it is perpendicular to the position of A relative to B according to time .

Do you follow me now, hence the pic I included, do u not agree that at some point it will be perpendicular and this represents the least distance…….

4. Sep 20, 2006

### Gokul43201

Staff Emeritus
Are you sure about this?

5. Sep 21, 2006

### ku1005

LOL....no not now, caus i know how smart u guys r!!! its just that thats the way i always hav done finiding that particular vector....so yes i am incorrect, since if you add them as "hallsofivy" stipulates, u obtain the answer, its just that i dont undertsand why it works, tats all....

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