Question

A man of height h is walking away from the street lamp of height 3h with constant speeh v find the rate at which of thr lenght of the shadow of the man is increasing when he is at a distance of 10h from the base of the lamp

Answer 1

Let the horizontal distance between lamp and person be a and the horizontal distance between person and shadow be b  From the figure: ΔABC and δADE are similar  DEBC=AEAC  ⇒3hh=a+bb  ⇒3b=a+b  ⇒a=2b  Differentiating on both sides w.r.t. t ∂a∂t=∂ 2b∂t  ⇒vman=2×vshadow  ⇒vshadow=v2