Firstly I apologise if my problem here seems a bit daft but I have got nobody other than myself or you guys to tell me if I'm doing things correctly or not.(adsbygoogle = window.adsbygoogle || []).push({});

The question:

Two cyclists are riding one along each of two perpendicular roads that meet at A. At one instance both cyclists are 500m from A and both are approaching A. If the speed of one of the cyclists is 8m/s, and the shortest distance between them is 50m find the two possible speeds of the other cyclist.

My attempt to solve:

http://img295.imageshack.us/img295/6594/question53ju.jpg [Broken]

The first diagram on the left represents how far P is away from Q initially and the second shows the line QR (the velocity of Q relative to P.

In the second diagram I know that the line PR is perpendicular to QR for this length to be the shortest distance, also since I know two lengths of this triangle I find the angle RQP to be 4.055degs.

In a triangle of vectors for velocity (I was in a rush and didn't transfer this from my work book, sorry) the angle that the line representing Q's relative velocity makes with it's true velocity is 45 + or - 4.055degs

Using 8/tan theta, the answers I finally end up with being 9.22m/s or 6.94m/s

My problem however is that the books answers are given as 6.9km/h or 9.23km/h (I take the km/h bits to be typo's)...and though this looks reasonably close to my answers, firstly one answer needed only to be given to 2sf whilst the other 3sf...secondly I could take potshots at this question and still arrive at an answer that is pretty close to mine or the book's, and so I cannot be sure that my working is correct. Have I done something wrong or should I chill out and move on to my next question?...If I am wrong can somebody give me a clue?

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# Shortest Distance Problem

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