Calculus Homework

Question

A street light is mounted at the top of an 18-ft-tall pole. A man 6ft tall walks away from the pole with a speed of 8ft/s along a straight path. How fast is the tip of his shadow moving when he is 30ft from the pole? (Hint: Use the Triangle Ratio to find the length of the tip of his shadow first.)

Answer 1

If D = the distance from the pole and L = the length of the shadow, it can be shown that

L = (1/2)D, which means that

dL/dt = (1/2)dD/dt

Since dD/dt = 8 ft/sec at any distance from the pole

dL/dt = (1/2)(8) = 4 ft/sec at any distance from the pole

From the pole, his shadow is moving at a rate of 8 + 4 = 12 ft/sec.