I travel 1 km east, than 1 km north, then climb 400m straight up a cliff. what is my distance from my starting point?
1469.7m
To determine your distance from the starting point, we can use the Pythagorean theorem.
1. First, let's visualize your movements on a Cartesian coordinate system. Start by placing the starting point at the origin (0, 0).
2. You travel 1 km east, which means you move one unit to the right on the x-axis. This brings you to a point at (1, 0).
3. Next, you travel 1 km north, which means you move one unit up on the y-axis. This brings you to a point at (1, 1).
4. Finally, you climb 400 meters straight up, which doesn't affect your position on the x or y-axis but only adds height in the z-axis. So, you remain at (1, 1), but now at a height of 400 meters.
5. Now, we can calculate the distance from the origin to your final position using the Pythagorean theorem, which states that the square of the hypotenuse (the distance between two points) is equal to the sum of the squares of the other two sides.
Applying this theorem to our scenario:
The horizontal displacement is 1 km or 1000 meters.
The vertical displacement is 400 meters.
Using the Pythagorean theorem:
Distance^2 = (Horizontal displacement)^2 + (Vertical displacement)^2
Distance^2 = 1000^2 + 400^2
Distance^2 = 1,000,000 + 160,000
Distance^2 = 1,160,000
Taking the square root of both sides, we find:
Distance = √1,160,000
Distance ≈ 1077 meters
Therefore, your distance from the starting point is approximately 1077 meters.