Question

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight line on the horizontal ground. The lamp post and the person are always vertical. If the speed of the person is 60 cm/sec, then find the speed of tip point of its shadow with respect to the person in cm/sec.

Answer 1

$\frac{x_1+x_2}{x_2}=\frac{4}{1.6}=\frac{5}{2}\Rightarrow\,x_2=\frac{2}{3}x_1$
$\frac{dx_2}{dt}=\frac{2}{3}\frac{dx_1}{dt}\, where \,\frac{dx_1}{dt}=60cm/sec.$
$\frac{dx_2}{dt}=(\frac{2}{3})(60)=40 cm/sec.$