A woman goes out running. She first travels 5.2km north. She then turns and travels 3.6km west. Finally, she turns again and travels 2.6km south. We are assuming a flat rectangular world.
If a bird were to start out from the origin (where the woman starts) and fly directly (in a straight line) to her final location, what distance d d would the bird cover?
D = 5.2i - 3.6 - 2.6i = -3.6+2.6i
D^2 = -3.6^2 + 2.6^2 = 19.72
D = 4.44 km.
To find the distance the bird would cover, we can use the Pythagorean theorem.
1. First, let's plot the woman's movements on a coordinate plane. We can set the starting point as the origin (0,0).
2. The woman first travels 5.2km north, so we move up 5.2 units on the y-axis. Her new position is (0, 5.2).
3. Then, she turns and travels 3.6km west. We move 3.6 units to the left on the x-axis. Her new position is (-3.6, 5.2).
4. Finally, she turns again and travels 2.6km south. We move 2.6 units down on the y-axis. Her final position is (-3.6, 2.6).
5. Now, we can calculate the distance between the origin and her final position using the distance formula.
The distance formula is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) is the origin (0,0) and (x₂, y₂) is the woman's final position (-3.6, 2.6).
6. Substituting the coordinates into the formula, we get:
d = √[(-3.6 - 0)² + (2.6 - 0)²]
= √[(-3.6)² + 2.6²]
= √[12.96 + 6.76]
= √19.72
≈ 4.44 km
Therefore, the bird would cover approximately 4.44 km to fly directly from the origin to the woman's final location.