A VERTICAL POST WITH SQUARE CROSS SECTION OF 1M X 1M IS SET SQUARELY ON A CUBICAL BLOCK 3M ON A SIDE. SUPPORT S FROM THE FLOOR TO THE SIDES OF THE POST AS DESIRED. FIND THE INSIDE LENGTH OF THE SHORTEST POSSIBLE SUPPORT.
To find the inside length of the shortest possible support, we need to consider the position of the vertical post and the size of the cubical block it is set on.
First, let's visualize the setup. We have a cubical block with sides measuring 3m each. The vertical post is set squarely on top of this block, meaning it is perpendicular to the ground. The cross-section of the post is square with dimensions 1m x 1m.
To understand the problem better, let's consider the different scenarios for placing the support:
1. One support on each side of the post: In this case, we would place a support on each side of the post, making contact at the corners of the 1m x 1m cross-section. This would require a support length equal to the diagonal of the square, which can be calculated using the Pythagorean theorem: diagonal = √(1^2 + 1^2) = √2 ≈ 1.41m.
2. One support at the center of each side of the post: In this scenario, we would place a support at the midpoint of each side of the post, resulting in four supports total. Each support would have a length equal to half of the side length of the post. Therefore, the length of each support would be 1m / 2 = 0.5m.
3. One support at the center of the base of the post: In this case, we would place a support at the center of the base of the vertical post, resulting in a single support touching the midpoint of the base. The length of this support would be equal to half the diagonal of the base of the post, which can be calculated using the Pythagorean theorem again: diagonal = √(1^2 + 1^2) = √2 ≈ 1.41m, so the support length would be roughly 1.41m / 2 = 0.71m.
From the three scenarios, we can see that the shortest possible support length is 0.5m when each side of the post is supported at its midpoint.
Thus, the inside length of the shortest possible support is 0.5 meters.