A lamp is located on the ground 10 m from a building. A man 1.8 m tall walks from the light toward the building at a rate of 1.5 m s⁻¹. What is the rate at which the man's shadow on the wall is shortening when he is 3.2 m from the building ? Give your answer correct to two decimal places. [0.58 m/s](adsbygoogle = window.adsbygoogle || []).push({});

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I tried using similar triangles first to find the height of the lamp but nothing came out of that.

http://img364.imageshack.us/img364/5294/manbuilding9vw.png [Broken]

let h be the height of the lamp

[tex]

{h \over{x+10}} = {1.8 \over {x+3.2}}[/tex]

[tex]

h = { {1.8x+18} \over {x + 3.2}}

[/tex]

How is the velocity of the man related to the height of the shadow? Or, what else should I find?

Also, shouldn't the shadow of the man on the wall become taller as he approaches the building?

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# Related rates and a lamp

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