question_answer

A man of height h walks in a straight path towards a lamp post of height H with velocity v. Then  velocity of the edge of the shadow on the ground will be

A) \[\frac{hv}{H+h}\]   

B) \[\frac{Hv}{H-h}\]

C) \[\frac{H+h}{Hv}\]       

D) \[\frac{\left( H-h \right)}{Hh}\]

Correct Answer: B

Solution :

as  \[\Delta \text{LOS}\]and \[\Delta \text{MPS}\] are similar so, \[\frac{H}{x}=\frac{h}{x-y}\Rightarrow \left( H-hz \right)x=Hy\] \[\Rightarrow \left( H-h \right)\frac{dx}{dt}=H\frac{dy}{dy}=Hv\] \[\Rightarrow {{V}_{S}}=\frac{Hv}{H-h}\]