Question

1. The problem statement, all variables and given/known data
I am a new physics student am having trouble with a sample problem from the book.
I have the answer (below) but I don't not understand how they are finding that number.
Please help.

In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves.

Answer 1

You may use the following displacements in any order: (a) , 2.0 km due east (directly toward the east); (b), 2.0 km 30° north of east (at an angle of 30° toward the north from due east); (c), 1.0 km due west. Alternatively, you may substitute either -b for b or -c for c. What is the greatest distance you can be from base camp at the end of the third displacement?

Reasoning:

Using a convenient scale, we draw vectors a, b, c, -b, and -c as in Fig. 3-7a. We then mentally slide the vectors over the page, connecting three of them at a time in head-to-tail arrangements to find their vector sum d. The tail of the first vector represents base camp. The head of the third vector represents the point at which you stop. The vector sum d extends from the tail of the first vector to the head of the third vector. Its magnitude d is your distance from base camp.

Answer 2

the answer is d=4.8 km, but how do they get it?

Answer 3

i will attach the pictures right now give me a second...

Answer 4

Basically, you have to pick three of the possible vectors that you are allowed to use, add them vectorially in a diagram and see how far from base camp that takes you.
Repeat this procedure with different groups of the three vectors and see which combination takes you furthest from base camp
In other words, use trial and error to find the best trio.

Answer 5

you can see that since they can be added ina ny order - the net displacement is the same.

SO

a cannot be swapped so you wil start by moving 2 km due east.

no to maximis the displacement you want to keep going generally in th esame direction so
swap c for - c this moves you 1 km further east.

Now b is moving generally east whereas -b would go back on yourself so use a+ -c + b