Mathematics: rate of change

2010-05-30 5:33 am
Find the rate of change of shadow and speed of the top of shadow:


圖片參考:http://farm5.static.flickr.com/4027/4649404203_9b23b76f37_b.jpg

回答 (2)

2010-05-30 7:37 am
✔ 最佳答案
(a) Let the length of shadow be L(t) and OP=x(t) at the time t seconds, then
L : L+x= 1.5 : 2.5, then L=3x/2
dx/dt=walking speed= 0.8
thus, dL/dt=(3/2)dx/dt= 1.2 (m/s)
(b) the speed of the top of her shadow=(d/dt)(L+x)=(d/dt)(5x/2)
=(5/2)*0.8= 2 (m/s)

2010-05-30 00:07:24 補充:
Sorry!忘了貼圖,補充說明如下:
O為lamppost底部位置, P為行人的位置, OP=x(t)=行人的position function
dx/dt=行人速度=0.8 m/s
2010-05-30 6:40 am
這是高中物理= =
可以用中文嘛?


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