A 2 m tall student walks away from the base of a 6 m streetlamp at a constant speed

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A 2 m tall student walks away from the base of a 6 m streetlamp at a constant speed. Let

x

be the distance (in meters) between the student and the lamp and let

s

be the length of the student’s shadow. Let

T=x+s

denote the distance from the lamp to the tip of the shadow. Which of the following must be true about the three rates

\dfrac{dx}{dt},\;\dfrac{ds}{dt},\;\text{and}\;\dfrac{dT}{dt}

at any instant while the student is walking? (a)

\dfrac{dx}{dt}<\dfrac{ds}{dt}<\dfrac{dT}{dt}

(b)

\dfrac{ds}{dt}<\dfrac{dT}{dt}<\dfrac{dx}{dt}

(c)

\dfrac{ds}{dt}<\dfrac{dx}{dt}<\dfrac{dT}{dt}

(d)

\dfrac{dT}{dt}<\dfrac{ds}{dt}<\dfrac{dx}{dt}