一道数学题,关于微分的.One of NASA's old satelites is falling back to the earth.When it lands,it will spash down into the ocean,making a circular ripple that will travel outward at a speed of 0.55m per second.Find the rate at which the area
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一道数学题,关于微分的.One of NASA's old satelites is falling back to the earth.When it lands,it will spash down into the ocean,making a circular ripple that will travel outward at a speed of 0.55m per second.Find the rate at which the area
一道数学题,关于微分的.
One of NASA's old satelites is falling back to the earth.When it lands,it will spash down into the ocean,making a circular ripple that will travel outward at a speed of 0.55m per second.Find the rate at which the area within the circle of the first ripple is increasing after 85 seconds.
一道数学题,关于微分的.One of NASA's old satelites is falling back to the earth.When it lands,it will spash down into the ocean,making a circular ripple that will travel outward at a speed of 0.55m per second.Find the rate at which the area
不考虑地球表面曲率影响,将洋面波当作平面波来计算.首先分析题目已知条件知圆半径r与时间t的关系：dr/dt=0.55,初始条件：当t=0时r=0.所有单位均取SI单位制.
解微分方程得到：r=0.55t
而面积S=πr²,两边取微分得到：
dS=2πrdr
将已知微分方程代入上述微分式得到：
dS=2πr(0.55dt)=1.1πrdt
整理得到：dS/dt=1.1πr
再把r与t的函数关系代入得到：
dS/dt=0.605πt
t=85s时的面积增长率为：
0.605π×85=161.5564 m²/s