A 4m tall lamppost stands on level ground. A child who is 1.2m tall walks directly away from the lamppost along the ground. Let
• x(t) be the horizontal distance (in meters) between the child and the base of the lamppost at time t seconds, and
• y(t) be the length (in meters) of the child’s shadow at that same instant.
(1) Part 1: (a) Using geometric reasoning, express y as an explicit function of x. Provide a clear statement of any proportion you establish and the algebraic steps that lead to your final relation.
(2) Part 2: (b) Describe how the shadow length y changes as the child moves farther from the lamppost. Support your description by referencing features of the formula you derived in part (a).