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AP Calculus AB· difficulty 3/5

A 6-ft person walks away from a 15-ft lamp post at 4 ft/s4~\text{ft/s}. How fast does the tip of the shadow move?

  • A

    4 ft/s4~\text{ft/s}

  • B

    2 ft/s2~\text{ft/s}

  • C

    10 ft/s10~\text{ft/s}

  • D

    203 ft/s\tfrac{20}{3}~\text{ft/s}

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Explanation

Similar triangles: tip distance T=x+sT = x + s with s/6=T/15s/6 = T/15, so T=(15/9)x=(5/3)xT = (15/9)x = (5/3)x. dT/dt=(5/3)(4)=20/3 ft/sdT/dt = (5/3)(4) = 20/3~\text{ft/s}.

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