Question
A bicyclist rides 22 km due north from home and then turns and rides 23 km due west. What is the displacement (on a straight line) of the bicyclist from home?
Answers
GPT-4o mini
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.
1. The distance traveled north (let's denote this as \(y\)) is 22 km.
2. 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.
1. The distance traveled north (let's denote this as \(y\)) is 22 km.
2. 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.