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.

Question

How fast is the tip of his shadow moving when he is 30 ft from the pole?

Answer 1

Let x is length of shadow and y is distance from man to pole. Then from cimilyarity of triangles: 15/6 = (y + x)/x; From here 5x = 2y + 2x; 3x = 2y; x = 2/3y; dx/dt = 2/3dy/dt = 2/3·5ft/s = 10/3 ft/s

Speed of tip of shadow independent of y and always constant 10/3 ft/s