A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the length of his shadow changing?

Question

A man 6 feet tall walks at a rate of  feet per second away from a light that is 15 feet above the ground (see figure). When he is  feet from the base of the light, at what rate is the length of his shadow changing?

Quizplus · Accepted Answer

Let's denote the length of the shadow as x. By similar triangles, we know:

(x+6)/6 = (15/11)

Solving for x, we get:

x = (54/11) feet

Now we can differentiate both sides with respect to time t:

d/dt(x+6)/6 = d/dt(15/11)

Simplifying, we get:

dx/dt = (-36/121) feet per second

Therefore, the rate of change of the length of his shadow is 11eaa595_661b_0c14_a696_e1796b56f4e1_TB4584_11_TB4584_11 ft/sec (Choice C).

A Man 6 Feet Tall Walks at a Rate of