Question

A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole

Answer 1

hi nikki
As the man goes farther from the street light, his shadow grows.



You can see if drow the diagram , that you have two similar right triangles



So, y/(y-x) = 15/6 and you can solve for y: y=5x/3.

Now differentiate both sides of this equation with respect to time t, then substitute in what you know for the values of the variables which are dx/dt ,y . Since you want the speed of the shadow, you want to find out what dy/dt equals.

Cheers,