Posted by Nikki on .
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
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.