How Do You Calculate Vector Distances on a Checkerboard?

[BlackMamba]

Hi again,

I have what is seems to be a simple vector addition problem, but I am questioning a certain part of it. I would show a diagram but I can't at the moment as the computer I am on does not have a drawing program. It should be fairly easy to picture though.

The base of the drawing is a checker board. Everyone knows what those look like, right? There is a force (a checker) A which crosses the black squares diagonally toward the direction of north of east. Then there is a force B (the same checker) which again crosses the black squares pointing in the direction of north of west. The tail of force A begins half way through one black square and the head ends half way into the last black square. Force A passes through 3 full squares, and only through half of 2 of them. Force B passes through 1 full square and only through half of 2 of them.

Each side of a square measures 4.9 cm.

So my question is to find the distance of forces A and B. Would it be easier to find the resultant of those squares. Then add them to find the length of A and B? Or would there be a better method of finding the length of A and B?

 

[BlackMamba]

Nevermind. The answer is yes. This thread could be deleted if need be. Sorry about that.

 

[M98Ranger]

Hi there! From what I understand, you have two forces, A and B, acting on a checker board grid. Force A is pointing northeast and passes through 3 full squares and 2 half squares. Force B is pointing northwest and passes through 1 full square and 2 half squares. You want to find the total distance of forces A and B.

To find the total distance of forces A and B, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can consider each full square as one side of the triangle and each half square as half of a side. So for Force A, the length would be (3*4.9) + (2*4.9/2) = 18.55 cm. For Force B, the length would be (1*4.9) + (2*4.9/2) = 7.35 cm.

Now, we can use the Pythagorean theorem to find the total distance of forces A and B. Let's call the total distance D. So D^2 = 18.55^2 + 7.35^2. Solving for D, we get D = 20.09 cm.

So the total distance of forces A and B is approximately 20.09 cm. I hope this helps! Let me know if you have any further questions.