Question

A street light is mounted at the top of a 15-ft tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

(the answer is 25/3 ft/s)

Answer 1

Let x be the man's distance from the pole. From geometry, the location of the tip of the shadow, p, as a function of x, is
\[p(x) = \frac{15}{15-6}x = \frac{5}{3}x\]
using the chain rule, we know that\[\frac{dp}{dt} = \frac{dp}{dx}\frac{dx}{dt}\]
so\[\frac{dp}{dt} = \frac{5}{3} * 5 = \frac{25}{3} ft/s\]

Answer 2

how did u get (15/15-6)x ?

Answer 3

in the book it says...