A student observes that when a pedestrian of height hp walks past a streetlamp of height hl(>hp), the streetlamp, the top of the pedestrian’s head, and the tip of the pedestrian’s shadow lie on a straight line.
(a) Identify two distinct pairs of corresponding angles that demonstrate the geometric similarity between the triangle formed by the streetlamp and the ground and the triangle formed by the pedestrian and the ground.
(b) Using the similarity established in part (a), express the length s of the pedestrian’s shadow in terms of the pedestrian’s distance d from the base of the streetlamp, hp, and hl. Do not perform any differentiation.
(c) Describe, in words, how the relationship found in part (b) can be used to connect the pedestrian’s walking speed to the rate at which the shadow length changes.