A six foot tall person is walking away from a 14 foot tall lamp post at 3 feet per second. When the person is 10 feet from the lamp post, how fast is the tip of the shadow moving away from the lamp post?

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Answer 1 · 2018-01-17T11:41:52

$sf(5.2color(white)(x)"ft/s")$

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We are told that:

$sf(dx/dt=3color(white)(x)"ft/s")$

We are asked to find $sf(dy/dt)$

From the geometry of the situation we need to find the relationship between x and y.

The man and the lamp post describe 2 similar triangles at any given instant such that:

$sf(14/y=6/((y-x)))$

$:.$ $sf(14(y-x)=6y)$

$sf(14y-6y=14x)$

$sf(8y=14x)$

$sf(y=14/8x)$

Differentiating implicitly both sides with respect to t $rArr$

$sf(dy/dt=14/8.dx/dt)$

$sf(dy/dt=14/8xx3=5.25color(white)(x)"ft/s")$