An athlete runs 2.76 km east, then turns south and runs another 0.85 km. What is the magnitude of his displacement?

2.76km[0o] + 0.85km[270o]

X = 2.76*Coso + 0.85*cos270 = 2.76 N.
Y = 2.76*sin0 + 0.85*sin270 =

Fr = sqrt(X^2+Y^2)

To find the magnitude of the athlete's displacement, we can use the Pythagorean theorem, as the displacements in the east and south directions are perpendicular.

First, let's draw a diagram to visualize the situation:

```
0.85 km
┏━━━━━━━━┓
┃ ┃
┃ ┃
┃ ┃ 2.76 km
┃ ┃
┃ ┃
┃ ┃
┃ ┃
┗━━━━━━━━┛
```

The athlete runs 2.76 km east, and then turns 90 degrees south and runs another 0.85 km.

Using the Pythagorean theorem, we can calculate the magnitude of the displacement as follows:

displacement = √(east displacement)² + (south displacement)²

east displacement = 2.76 km
south displacement = 0.85 km

displacement = √(2.76 km)² + (0.85 km)²
= √(7.6576 km² + 0.7225 km²)
= √8.38 km²
= 2.895 km (rounded to three decimal places)

Therefore, the magnitude of the athlete's displacement is approximately 2.895 km.

To find the magnitude of the athlete's displacement, we can use the Pythagorean theorem. The displacement is essentially the straight-line distance between the starting point and the final point.

First, let's break down the athlete's motion into horizontal and vertical components. The athlete runs 2.76 km east and then turns south and runs 0.85 km. The east direction represents the horizontal component, and the south direction represents the vertical component.

We can create a right-angled triangle using these two components. The horizontal component (2.76 km) will be the adjacent side, and the vertical component (0.85 km) will be the opposite side. The displacement will be the hypotenuse of the triangle.

To find the magnitude of the displacement, we can use the Pythagorean theorem:

displacement^2 = (horizontal component)^2 + (vertical component)^2

displacement^2 = (2.76 km)^2 + (0.85 km)^2

displacement^2 = 7.6176 km^2 + 0.7225 km^2

displacement^2 = 8.34 km^2

Now, we can take the square root of both sides to find the displacement:

displacement = sqrt(8.34 km^2)

Using a calculator, we find:

displacement ≈ 2.89 km

Therefore, the magnitude of the athlete's displacement is approximately 2.89 km.