AP微积分题目.A street light is at the top of a 12.0 ft. tall pole. A man 5.0 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 42 feet from the pole?只给答

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AP微积分题目.A street light is at the top of a 12.0 ft. tall pole. A man 5.0 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 42 feet from the pole?只给答
AP微积分题目.
A street light is at the top of a 12.0 ft. tall pole. A man 5.0 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 42 feet from the pole?
只给答案也可以.为什么我反复算都说45/14但是不对.

AP微积分题目.A street light is at the top of a 12.0 ft. tall pole. A man 5.0 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 42 feet from the pole?只给答
设从灯到人的距离为x,人到灯影子最前端距离为y
用相似三角形得5/12=y/x+y
所以5/7=y/x
也就是x=7y/5
已知x=4.5t
所以4.5t=7y/5
等号两边同时关于t求导,得4.5=(7/5)*dy/dt
所以dy/dt=45/14
但是,dy/dt并不是影子最前端移动的速度,因为人的位置,也就是影子末端的位置,也在动
所以最后答案应该是dy/dt+dx/dt=45/14+4.5=54/7

v1/v2=(12-5)/12=7/12
v1=4.5
于是v2=54/7

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