> For the complete documentation index, see [llms.txt](https://xu-shi-min.gitbook.io/untitled/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://xu-shi-min.gitbook.io/untitled/ch3-wei-fen-de-ying-yong/3.6-zui-jia-hua-wen-ti.md).

# \*3.6 最佳化問題

課本例4類題\
一段筆直海岸附近的海上點A處有一艘船，岸邊與點A最近的點為點B，點A與點B的距離為2公里。瑪雅坐在船上，晀望岸邊一個與點B距離6公里的村莊，這村莊是瑪雅的目的地。她打算用 2 公里/小時的速度划船，在點B與村莊之間的某處上岸之後，馬上用 5 公里/小時的速度跑步。請問，她該把船停在離點B多遠的地方，才能用最短的時間到達村莊呢？\
(請沿著海岸線拖曳點 P，可以看到完成行程所需的總時間如何變化。紅色跑者是用最短的時間的情況，就是本題的答案。)

<figure><img src="https://2411550807-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkDziKgvSMwwzgTvHrbcW%2Fuploads%2FcYBp83ADtCGyJWd711K4%2F00.png?alt=media&amp;token=8a90b945-9630-4b1f-be30-5f4034a2bde5" alt=""><figcaption></figcaption></figure>

{% embed url="<https://www.geogebra.org/m/he5Za34U>" %}
<https://www.geogebra.org/m/he5Za34U>
{% endembed %}

課本習題26

<figure><img src="https://2411550807-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkDziKgvSMwwzgTvHrbcW%2Fuploads%2F9VCTvu85wIlsKpHAM84W%2Fimage.png?alt=media&amp;token=9517221d-2b83-43c8-99bf-6e8227e6cd30" alt=""><figcaption></figcaption></figure>

解答提示：

<figure><img src="https://2411550807-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkDziKgvSMwwzgTvHrbcW%2Fuploads%2FSw9vjQpIfKuRQ9TbB3CN%2Fimage.png?alt=media&amp;token=76c3a81b-5005-4c51-ada4-c056e6517013" alt=""><figcaption></figcaption></figure>

課本習題26參考程式

<figure><img src="https://2411550807-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FkDziKgvSMwwzgTvHrbcW%2Fuploads%2FN3FlDPKMp7nuJ40UzbJA%2Fimage.png?alt=media&amp;token=843a3ca0-cc3a-4766-8872-2a0b5873412e" alt=""><figcaption><p>空氣折射率~1  水折射率~1.33</p></figcaption></figure>

{% embed url="<https://www.geogebra.org/m/qMvN2Rzz#material/YxnbW85K>" %}
<https://www.geogebra.org/m/qMvN2Rzz#material/YxnbW85K>
{% endembed %}