Charlie, who is 5 feet tall, walks away from a streetlight that is 16 feet high at a rate of 6 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time. (Hint: First use similar triangles to express s as a function of the distance d from the streetlight to Charlie.)

Question

Mathematics

Hailie Ruiz

29 April, 13:42

Charlie, who is 5 feet tall, walks away from a streetlight that is 16 feet high at a rate of 6 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time. (Hint: First use similar triangles to express s as a function of the distance d from the streetlight to Charlie.)

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Adolfo Norman · Answer 1

Given:

Height of Charlie: 5 feet

Height of street light: 16 feet

Rate of movement: 6 feet/s

Illustrate the problem by drawing two similar triangles. The first leg of triangle 1, the height of the street light. The first leg of triangle 2, the height of Charlie. The shadow is moving at y ft/s. The distance between Charlie and the light is also moving at x ft/s.