To find the displacement of the bicyclist from home after riding 22 km north and then 23 km west, we can use the Pythagorean theorem.
- The distance traveled north (let's denote this as \(y\)) is 22 km.
- The distance traveled west (let's denote this as \(x\)) is 23 km.
The displacement \(d\) can be calculated using the formula: \[ d = \sqrt{x^2 + y^2} \]
Substituting the values: \[ d = \sqrt{(23, \text{km})^2 + (22, \text{km})^2} \] \[ = \sqrt{23^2 + 22^2} \] \[ = \sqrt{529 + 484} \] \[ = \sqrt{1013} \] \[ \approx 31.8, \text{km} \]
Therefore, the displacement of the bicyclist from home is approximately 31.8 km in a straight line.