# Vectors help

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• Sep 13th 2011, 04:09 AM
ilovemaths321
Vectors help
Boat A has initial position (-8,9) and has a velocity vector [4,-1].
Boat B has initial position (1.-9).

Boat B has a maximum speed of 8km/h. Determine the time and velocity vector [a,b] for the collision to occur as soon as possible.

So hard..don't know how to do it.
• Sep 13th 2011, 07:49 AM
emakarov
Re: Vectors help
There may be other ways.

Step 1. Let t be the time to the collision. Using a and b, write two equations on t. Dividing one equation by the other, you cat get a linear relation between a and b: they have to satisfy this relation in order for the boats to meet.

Step 2. Allowed points (a, b) are inside the circle with center (0, 0) and radius 8. The circle cuts a segment from the line obtained in step 1. Each point on the segment gives rise to some t; you need to find the point with the smallest t.

Step 3. From one of the equations from step 1 express t through a and draw a graph of t(a). Find the minimum of t when a belongs to the segment found in step 2.
• Sep 14th 2011, 02:30 AM
ilovemaths321
Re: Vectors help
Sorry, I still don't understand. I'm pretty dumb.
• Sep 14th 2011, 02:33 AM
emakarov
Re: Vectors help
Let's take it one step at a time.
Quote:

Originally Posted by emakarov
Let t be the time to the collision. Using a and b, write two equations on t.

If you can do this, write the first thing in the outline from post #2 that you are having trouble with.
• Sep 14th 2011, 02:39 AM
ilovemaths321
Re: Vectors help
What do you mean "write two equations on t"?
• Sep 14th 2011, 02:46 AM
emakarov
Re: Vectors help
The values a, b and t are related by the fact that there is an encounter in t hours. In the horizontal direction, boat B, which moves right at a km/h, starts 1 - (-8) = 9 km to the right of boat A, which moves right at 4 km/h. The fact that they meet in t hours gives an equation that uses a and t. Similarly, there is an equation for the vertical direction.
• Sep 14th 2011, 03:10 AM
ilovemaths321
Re: Vectors help
Quote:

Originally Posted by emakarov
The fact that they meet in t hours gives an equation that uses a and t.

Hmm...I don't know how to construct the equation.
• Sep 14th 2011, 03:16 AM
emakarov
Re: Vectors help
The relative speed at which A catches up with B is 4 - a. There are 9 km to catch up in t hours.

Alternatively, boat A will be at x-coordinate -8 + 4t in t hours. Similarly, boat B will be at 1 + at. These coordinates coincide when they meet.
• Sep 14th 2011, 03:21 AM
ilovemaths321
Re: Vectors help
Quote:

Originally Posted by emakarov
The relative speed at which A catches up with B is 4 - a. There are 9 km to catch up in t hours.

Alternatively, boat A will be at x-coordinate -8 + 4t in t hours. Similarly, boat B will be at 1 + at. These coordinates coincide when they meet.

So the y-coordinate for boat A would be 9-t and for boat B would be -9+bt ?
• Sep 14th 2011, 03:22 AM
emakarov
Re: Vectors help
Yes.
• Sep 14th 2011, 03:39 AM
ilovemaths321
Re: Vectors help
Okay, so now do I equate them?
• Sep 14th 2011, 03:41 AM
emakarov
Re: Vectors help
I am sure they won't blow up if you do (Smile)
• Sep 14th 2011, 03:45 AM
ilovemaths321
Re: Vectors help
Quote:

Originally Posted by emakarov
I am sure they won't blow up if you do (Smile)

I got: a=(-9/t)+4 and b=(18/t)-1 (Thinking)
• Sep 14th 2011, 03:48 AM
emakarov
Re: Vectors help
My original idea was to eliminate t and to express b through a.
• Sep 14th 2011, 04:06 AM
ilovemaths321
Re: Vectors help
Quote:

Originally Posted by emakarov
My original idea was to eliminate t and to express b through a.

How do I eliminate t?
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