Question

A man of height $1.5meter$ is moving away from a lamppost at the rate $1.2meterpersec$. If the height of the lamppost is $4.5meter$. Find the rate at which
i) his shadow is lengthening.
ii) the tip of his shadow is moving.

Answer 1

Consider the following figure.

Given ,

$\frac{dx}{dt}=1.2m/s$

From similarly of both triangle $\left(\Delta AOB\&\Delta DOC\right)$

$\begin{array}{c}\frac{1.5}{L-k}=\frac{4.5}{L}\\ LSL=4.5L-4.5x\\ 4.5x=3L\\ Hence,\frac{dL}{dt}=1.5\times 1.2=1.8m/s\end{array}$

Hence, $tip\left(0\right)$ is moving with $1.8m/s$

Shadow is Lenghtening with $(1-x)=0.6m/s$