Question

Jerry lives in a city where all the roads are organized into square blocks and the roads either run North/South or East/West (forming a big square grid). Jerry goes out walking one day. He starts by walking 3 blocks North and then 4 blocks East. Jerry next walks 2 blocks South and 1 block West, when he realizes it is getting late and he must get home quickly. If Jerry walks on the roads home using as few blocks as possible, how many blocks will it take?

Answer 1

it will take Jerry 4 blocks to get home. 3 blocks West and 1 block South

Explanation:

We use our vector notation to describe the problem. Since Jerry walks 3 blocks North, he moves in the direction 3j. He then walks 4 blocks East in the direction 4i. He walks 2 blocks South in the direction -2j and 1 block West in the direction -i.

So, his position vector r = 3j + 4i - 2j - i = 4i - i + 3j - 2j = 3i + j.

Now if we assume his home was at the origin, then his initial position r₀ = 0i + 0j

Since he is supposed to return home from his current position, his displacement is final position - initial position = r₀ - r = 0i + 0j -(3i + j) = 0i - 3i + 0i - i = -3i - j

Since -i means movement in the West direction, -3i means movement 3 blocks West.

Since -j means movement in the Southern direction, -j means movement 1 blocks South.

So, it will take Jerry 1 + 3 blocks = 4 blocks to get home. 3 blocks West and 1 block South