Final answer:
The magnitude of the archaeologist's displacement after climbing the Great Pyramid is found using the Pythagorean theorem, considering the path as the hypotenuse of a triangle formed by the height of the pyramid and half of its base width. The direction is diagonally upward towards the center of the pyramid from the starting corner.
Step-by-step explanation:
The question asks for the magnitude and direction of the displacement of an archaeologist after she has climbed from the bottom to the top of the Great Pyramid in Giza, whose height is given as 136 meters and its width (which can be assumed to be the length of one side of the pyramid's base) is given as 2.30 x 101 meters (or 230 meters).
To find the displacement, we treat the climb as a straight-line path from the bottom of the pyramid (at one corner of the base) to the top. The displacement vector forms the hypotenuse of a right triangle whose legs are the height of the pyramid and half the width (which would be the distance from a corner to the center of the base).
Let's calculate the displacement using the Pythagorean theorem:
- First, calculate half the width of the base: 230 meters / 2 = 115 meters.
- The displacement's magnitude (d) can then be found using the formula: d = √(height2 + (half-width)2)
- Plugging the values in, we get: d = √(1362 + 1152) meters
- Calculating this gives the magnitude of displacement.
The direction of the displacement vector would be upwards and towards the center of the pyramid's base from the starting corner. If we define the direction towards the center of the base as 'inward' and upward as 'upward,' the resultant direction is a diagonal line joining these two directions.
The magnitude and direction of displacement would fully describe the archaeologist's change in position from the bottom to the top of the pyramid.