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The Two Yachts Problem

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Introduction

The Two Yachts Problem

Pg. 405                                                        IB Math SL Y2

Yacht A has initial position (-10, 4) and has velocity vectorimage00.png.

Yacht B has initial position (3, -13) and has velocity vectorimage01.png.

1. Explain why the position of each yacht at time t is given by

           rA = image03.png

...read more.

Middle

. (image18.png refers to an initial position and image02.png refers to a direction vector.)

- Therefore, a vector equation for Yacht A can be written as image03.png+ timage00.png.

- A vector equation for Yacht B can be written as image04.png+ timage01.png.

3.

...read more.

Conclusion

So, 50t - 214 = 0. Thus t = image11.png= 4.28.

6. The time when d is to be a minimum is the same time as when d2 is a minimum, so the closest approach occurs at t = 4.28. So, if I put t = 4.28 into the expression for d is:

d =image10.png

  = image12.png

= image13.png

  = image14.png

  =  0.2 miles

...read more.

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