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 3 h. The rate at which the length of the boy's shadow is increasing when he is at a distance of 10 h from the base of the street lamp is:                        

A) 2v

B) v     

C) v/2  

D) v/3

Correct Answer: C

Solution :

[c] 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 \[=\frac{h}{x}=\frac{3h}{x+y}\text{ or }x=y/2.\] \[\text{Thus }\frac{dx}{dy}=\frac{dy/dt}{2}\]