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?

Question

27966 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-17T11:41:52

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

MfDocs

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")#