question_answer

A boy of height \[h\] is walking away from a street lamp with a constant speed v. the height of the street lamp is \[3h\]. The rate at which the length of the boy's shadow is increasing when he is at a distance of \[10h\] from the base of the street lamp is:

A) \[2v\]                            

B) \[v\]

C) \[v/2\]   

D) \[v/3\]

Correct Answer: C

Solution :

let x be the length of the shadow of the boy, when he is at a distance y from the lamp. From similar triangles, we have

\[\frac{h}{x}=\frac{3h}{x+y}\]

Or \[x=y/2\]

Thus \[\frac{dx}{dt}=\frac{dy/dt}{2}\]