Question

Help please and thanks

Answer 1

Rate of change of length of shadow is
`(15)/(7) ft/s`

Explanation:

Consider the figure

We have

`\begin{aligned}&(d x)/(d t)=\text { rate of person walking } \\&(d y)/(d t)=\text { rate of change of shadow length } \\&(d x)/(d t)+(d y)/(d t)=\text { rate of change of tip of shadow }\end{aligned}`

`\begin{aligned}&(6)/(20)=(y)/(x+y) \\&6(x+y)=20 y \\&6 x+6 y=20 y \\&6 x=14 y\end{aligned}`

`6\left((d x)/(d t)\right)=14\left((d y)/(d t)\right)\\\\6(5)=14\left((d y)/(d t)\right)\\\\(30)/(14)=(d y)/(d t)\\\\(15)/(7)=(d y)/(d t)\\\\`

Rate of change of length of shadow is
`(15)/(7) ft/s`