# Vectors help

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• Sep 14th 2011, 05:08 AM
emakarov
Re: Vectors help
Express t from one equation and substitute in into the other.
• Sep 14th 2011, 05:16 AM
ilovemaths321
Re: Vectors help
Quote:

Originally Posted by emakarov
Express t from one equation and substitute in into the other.

I don't know if this is right but I ended up with b= -2a+7
• Sep 14th 2011, 05:27 AM
emakarov
Re: Vectors help
Yes. Also, you probably got that t = 9 / (4 - a). The latter graph looks like this. So, for a > 4 the time to meeting is negative, which means that the meeting must have been in the past and will not happen in the future (this is natural since if B moves right faster than A, they cannot meet). For a < 4, the function t(a) is increasing. Since we need to find the smallest t, we need to find the smallest allowed a.

Since the maximum speed of B is 8 km/h, the vector (a, b), when its beginning is at (0, 0), lies inside a circle of radius 8. Also, b= -2a+7. The circle carves a segment on the line b = -2a+7, and we need to take the left end of that segment, which corresponds to the smallest a.
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