Optics Question 797
Question: 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:
Options:
A) 2v
B) v
C) v/2
D) v/3
Show Answer
Answer:
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} $
