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1、专题：小船过河问题分析1Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.要使船能在最短时间内渡河，则最短时间是 多少秒？应向何方划船？【例1】小船在d=200m宽的河水中行驶，船在 静水中
2、v划=4m/s，水流速度v水=2m/s。求：dV划 v实v水解： 应向对岸划行,航向角 =90.要使航线最短，那么应向何方划船？渡河 时间是多少秒？2Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty
3、 Ltd.要使航线最短，那么应向何方划船？渡河 时间是多少秒？dv2vv1(注意：V1=V水对地=V水 V2=V船对水=V划=V船 ：航向角（划行速度与河岸的夹角）d: 河的宽度V=V船对地=V实3Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyri
4、ght 2004-2011 Aspose Pty Ltd.1.最短时间过河2.最短位移过河过河时间最短；t = d / v划过河路径最短；s = d (v划v水)重要结论-小船的两种过河方式dV划v实v水dV划v实v水4Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty
5、 Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例2】小船在d=200m宽的河水中行驶，船在 静水中v2=2m/s，水流速度v1=4m/s。求：要使 船的航线最短，应向何方划船？位移的最小值 如何？ Sd v2vv1(）又(5Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright
6、2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.点评：当v2v1(v划v水）时，合速v不 可能垂直河岸。此时，以v1矢量的终 点为圆心，v2的大小为半径画圆，当 v与圆相切时，角最大，角最小， 则渡河航线最短，并且；6Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.
7、0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例3】汽船顺流从甲地到乙地，历时3h， 返回时需6h，如汽船关闭发动机顺流从甲地 漂到乙地，则所需时间为( ) A3h B6h C9h D12hD7Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile
8、 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例4】游泳运动员以恒定的速率垂直河岸 横渡当水速突然增大时，对运动员横渡经 历的路程、时间发生的影响是( ) A路程增长、时间增长 B路程增长、时间缩短 C路程增长、时间不变 D路程与时间均与水速无关C8Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.S
9、lides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例5如图4-3所示，在一光滑水平面上放 一个物体，人通过细绳跨过高处的定滑轮 拉物体，使物体在水平面上运动，人以大 小不变的速度v运动.当绳子与水平方向成 角时，物体前进的瞬时速度是多大？图4-39Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile
10、5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.应用合运动与分运动的关系 绳子牵引物体的运动中，物体实际在水平面上运动，这个 运动就是合运动，所以物体在水平面上运动的速度v物是合 速度，将v物按如图4-6所示进行分解.其中:v=v物cos，使 绳子收缩.v=v物sin,使绳子绕定滑轮上的A点转动. 所以v物=图4-610Evaluation only.Evalu
11、ation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例6】一只船从河岸A处渡河 ，河宽d=30m， v水=10m/s，距A 40m的下游有瀑布，为使小船 靠岸时，不至被冲进瀑布中，船的划行的最小 速度为多少？船的实际速度是多大？瀑
12、布xAv水SdV划v实(11Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例7】有一艘船以v甲的船速用最短的时间 横渡过河，另一艘船以v乙的船速从同一地点 以最短的距离过河，两船的轨迹
13、恰好重合（ 设河水速度保持不变），求两船过河所用时 间之比。12Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例8】某人乘船横渡一条河，船在静水中的 速度及水速一定，此人过河最短时间T
14、1，若 此船用最短的位移过河，所需时间T2，若船 速大于水速，则船速与水速之比为？13Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.【例9】有人驾船从河岸A处出发，如果使船头 垂直河岸航
15、行，经10min到达正对岸下游120m 的C处；若使船头指向与上游河岸成角的方向 航行，经12.5min到达正对岸的B点，求水速u ，航向 ，船速v，河宽d 水速u= 12m/min ，航向= 53 ，船速v= 20m/min ，河宽d =200m 。14Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 20
16、04-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.练习1如图所示，A、B两车通过细绳跨接在定 滑轮两侧，并分别置于光滑水平面上，若 A车以速度v0向右匀速运动，当绳与水平 面的夹角分别为和时，B车的速度是多 少？图4-11.vB=vB= 15Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty
