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# The Two Yachts Problem

Extracts from this document...

Introduction

The Two Yachts Problem

Pg. 405                                                        IB Math SL Y2

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

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

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

rA =

Middle

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

- Therefore, a vector equation for Yacht A can be written as + t.

- A vector equation for Yacht B can be written as + t.

3.

Conclusion

So, 50t - 214 = 0. Thus t = = 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 =

=

=

=

=  0.2 miles

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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