Question

一道数学题目，关于相关变化率的，跪求讲解~

A man 1.8m tall is walking at the rate of 0.9m/s toward a streetlight pole 5.4m igh.(a)At what rate is his shadow length decreasing?(b)How fast is the tip of his shadow moving?

Answer 1

AB=5.4，CD=C'D'=1.8，经过t时间后CD移动到C'D'，则CC'=0.9t，设影长EC为x，由相似三角形可以得到，BE=3x，则BC=2x，从而C'B=2x-0.9t，再根据相似三角形得到E'C'=x-0.45t，

EE'=EB-E'B=1.35t。

（1）求影子缩短的速率。经过t时间，影子长度由EC变为E'C'，故（EC-E'C'）/t=0.45

（2）求影子顶端的移动速率。经过t时间，影子顶端由E运动到E'，则EE'/t=1.35

Answer 2

太牛了