Question

A man $1.5m$ tall walks away from a lamp post $4.5m$ high at a rate of $4km/hr$. How fast is the farther end of shadow moving on the pavement?

• A. $4km/hr$
• B. $2km/hr$
• C. $6km/hr$
• D. $5km/hr$

Answer 1

Answer: (C)

Let $AC$ be pole, $DE$ be man and $B$ be farther end of shadow as shown in figure From triangles $ABC$ and $DBE$
$\frac{4.5}{x+y}=\frac{1.5}{y}$
$3y=1.5x$

$\frac{dy}{dt}=2,(x+y)=\frac{dx}{dt}+\frac{dy}{dt}$