某人蕩秋千,秋千踏板在靜止時離地0.3米,秋千蕩起時,踏.
某人蕩秋千,秋千踏板在靜止時離地0.3米,秋千蕩起時,踏.
某人蕩秋千,秋千踏板在靜止時離地0.3米,秋千蕩起時,踏板擺動的最大水平距離(兩最高點間的距離)為5米,踏板離地最大高度為1.3米,求秋千的繩長
正確答案: 知識點:幾何證明計算
思路和過程
繩長認為是不變的,可以抽象為等腰三角形和圓的問題求解。
AB = 5,CD = 1.3-0.3 = 1,AD= 2.5
OA=OB=OC=r (即繩長)
OD = r-1
根據勾股定理 (r-1)² + 2.5² = r² 解出
r = 29/8
![](data:image/png;base64,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)
正確答案: 知識點:幾何證明計算
思路和過程
繩長認為是不變的,可以抽象為等腰三角形和圓的問題求解。
AB = 5,CD = 1.3-0.3 = 1,AD= 2.5
OA=OB=OC=r (即繩長)
OD = r-1
根據勾股定理 (r-1)² + 2.5² = r² 解出
r = 29/8
你發的題目每一道都有答案提示,這很好,值得表揚!大大提高了回帖的準確性和速度。不過有一點值得改進,那就是不必凌晨1:00了還發那么多,要注意休息啊
把它想象一下,可以得出,當秋千到達最高位置時,離踏板最低點的水平距離為(1.3-0.3)=1米,這一點到靜止時繩子的距離為5/2=2.5米。把它想象成一個直角三角形,繩長即為斜邊,那么繩長為 (r-1)2 + 2.52 = r2
7.25=2r
解得繩長為3.625米
源于查字典網
把它想象一下,可以得出,當秋千到達最高位置時,離踏板最低點的水平距離為(1.3-0.3)=1米,這一點到靜止時繩子的距離為5/2=2.5米。把它想象成一個直角三角形,繩長即為斜邊,那么繩長為 (r-1)2 + 2.52 = r2
7.25=2r
解得繩長為3.625米