Auron 10 Posted November 9, 2007 Report Share Posted November 9, 2007 白日依山盡 黃河入海流欲窮千里目 更上一層樓Q:假設一層樓為4M那麼想要欲窮千里目 必須更上幾層樓 Link to post Share on other sites
我不嘴砲的 10 Posted November 10, 2007 Report Share Posted November 10, 2007 白日依山盡 黃河入海流欲窮千里目 更上一層樓Q:假設一層樓為4M那麼想要欲窮千里目 必須更上幾層樓我看到有人回答你了說...在"三角問題"那一篇可能是回錯了吧..真奇妙 Link to post Share on other sites
ccctheworld 10 Posted November 10, 2007 Report Share Posted November 10, 2007 因為地平線有弧度的~但角度很小=>sinθ≒θ≒tanθRθ=1000.R=6300...θ=10/63設樓高H H/100=tanθ≒ θH=1000/63 =15.87 ≒ 16H/4 = 4所以答案是4層樓@@PS剛放錯地方= = Link to post Share on other sites
Auron 10 Posted November 10, 2007 Author Report Share Posted November 10, 2007 真的只有4層樓嗎能不能把算式用簡單一點阿 Link to post Share on other sites
cj2340 10 Posted November 11, 2007 Report Share Posted November 11, 2007 Rθ=1000.R=6300...θ=10/63能不能說明一下這部分? Link to post Share on other sites
Auron 10 Posted July 17, 2008 Author Report Share Posted July 17, 2008 因為地平線有弧度的~但角度很小=>sinθ≒θ≒tanθRθ=1000.R=6300...θ=10/63設樓高HH/100=tanθ≒ θH=1000/63 =15.87 ≒ 16H/4 = 4所以答案是4層樓@@能不能說明一下這部分?R≒地球半徑(有誤差)這樣我了解了感謝學長 Link to post Share on other sites
Esther Chang 10 Posted July 17, 2008 Report Share Posted July 17, 2008 意見不同 不好意思喔~(我算出來跟4層樓差太多了)H/100是為什麼?沒看懂不好意思糾正一下我錯哪吧~意思是可以最遠看見距離所在處約500km(古代一里約500m)我的淺見因為角度太小同上採近似(弧長約等於切線段長)又H*(H+2R)=500^2又近似 故H*2R=500^2H約等於19.8km所以19.8*1000/4=4950 至少要4950層樓(R同上使用6300 應該比較接近6400才對) Link to post Share on other sites
Auron 10 Posted August 27, 2008 Author Report Share Posted August 27, 2008 又H*(H+2R)=500^2又近似 故H*2R=500^2H約等於19.8km所以19.8*1000/4=4950 這段能不能加以解釋 Link to post Share on other sites
Xiang 10 Posted August 27, 2008 Report Share Posted August 27, 2008 嗯,我剛剛去查了一下中國古代的一里大約是500公尺沒錯千里=500km首先先驗證角度極小為了方便計算,地球半徑採用6400kmθ=500/6400=0.078(弧度)←大約4度而已這時就可以使用sinθ≒tanθ≒θ附上圖方便看(角度沒那麼大)cosθ=0.99694357130932942287077314837634(自己按計算機)(R+H)cosθ=R,H=R(1-cosθ)=6400*0.003056428690670577129226851624=19.56大約5層吧,跟上面4層差不多,主要差在半徑取多少維基寫地球半徑大約6,372.797km,可以參考一下另外這題應該比較偏物理以純物理來解這樣大概是沒有什麼問題但是要牽扯到國文就有大大的問題了題目寫要「更上幾層樓」,原本是幾樓就很重要不過除非到數千樓倒是不會有什麼影響啦 Link to post Share on other sites
源良 10 Posted September 8, 2008 Report Share Posted September 8, 2008 H=R(1-cosθ)=6400*0.003056428690670577129226851624=19.56但19.56的單位是km呢看來他要跑半天少能窮千里目了 Link to post Share on other sites
hellwd0217 10 Posted September 8, 2008 Report Share Posted September 8, 2008 答案是看不見 因為太陽下山了(來亂:P) Link to post Share on other sites
Esther Chang 10 Posted September 9, 2008 Report Share Posted September 9, 2008 這段能不能加以解釋當H<<2R時這是採近似值啦!^^至於要問的是為什麼有這個式子的話該怎麼說的(我記得數學有這個公式 叫什麼來著...)你畫個圓 作圓外一點過點畫進圓到圓周(會有兩點!)點到那兩點的乘績會等於切線長的平方(我頹了很久... 忘了怎麼證明的><") Link to post Share on other sites
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