A beautiful Princess is locked inside the Castle. A Moat 15 metres wide surrounds the Castle.
A Knight is attempting to rescue the Princess but he only has two planks of wood, both 14.5 metres long.
How can the brave Knight bridge the Moat and rescue the Princess.
Draw diagrams and explain clearly all the calculations you make.
If the moat is of width ‘a’ and the planks are of length ‘b’ where b<a, show that the Knight will still be able to cross the moat provided b>0.94a
The knight must put the first plank diagonally across the corner of the moat, then put the second on the first.
Cannot diagram here.
To help the Knight rescue the Princess, we can use the two planks of wood to create a bridge across the 15-meter wide moat.
First, let's visualize the situation by drawing a diagram:
```
|------------------------------|
| Moat (width 'a') |
|------------------------------|
| Castle |
|-----------| |-----------| |
| | | | |
| | | | |
|-----------| |-----------| |
```
In this diagram, the Moat has a width 'a' (15 meters) and the two planks have a length 'b' (14.5 meters). We need to find a way to bridge the Moat using the planks.
Let's consider the scenario where b > 0.94a. This means that the length of the planks is greater than 0.94 times the width of the Moat.
To bridge the Moat, we will place one plank diagonally across the Moat, from one corner of the Castle to the opposite corner of the Moat. The other plank will be placed diagonally from the remaining corner of the Castle to the opposite corner of the Moat.
Using Pythagoras' theorem, we can calculate the length of the diagonal of a rectangle (in this case, the Castle):
diagonal^2 = length^2 + width^2
Since the Castle is rectangular, and the width is a, the diagonal of the Castle can be calculated as:
diagonal = sqrt(2 * a^2)
For a rectangular plank with length b and width a, the diagonal can be calculated as:
diagonal = sqrt(b^2 + a^2)
Now, let's calculate the length of the diagonal of one of the planks:
diagonal = sqrt(b^2 + a^2) = sqrt((14.5)^2 + (15)^2) = sqrt(210.25 + 225) = sqrt(435.25)
Therefore, the length of the diagonal of one plank is approximately 20.85 meters.
Since we placed one plank diagonally from one corner to the opposite corner of the Moat, the length of the bridge created by the plank on each side of the Moat will be half of the diagonal length, which is approximately 10.43 meters.
Now, let's verify if the Knight will be able to cross the Moat using the planks.
Since b > 0.94a, we can see that 14.5 > 0.94 * 15.
The length of each bridge created by a plank is approximately 10.43 meters, which is greater than the width of the Moat, 15 meters.
Therefore, the Knight will be able to cross the Moat and rescue the Princess using the two planks of wood, provided that the length of the planks is greater than 0.94 times the width of the Moat.
It is important to note that in this scenario, the planks are perfectly aligned and placed diagonally across the Moat to form the bridge. If the planks are not aligned at their ends, additional support or adjustments may be necessary.