A 7ft tall person is walking away from a 20 ft tall lamppost at what rate of 5ft/sec. at what rate... the lamppost?

Question

A 7ft tall person is walking away from a 20 ft tall lamppost at a rate of 5ft/sec. Assume the scenario can be modeled by right triangles. At what rate is the length of the persons shadow changing when the person is 16ft from the lamppost?

Answer 1

I'm not sure if I miss something here, i'll tell you why i'm skeptic later.

 

The drawing of this is just a right triangle, your choice where it is facing, with a height of 20 and place another vertical line inside the triangle that is reaching the hypotenuse and the base, and that is the 7. There will be two parts on the base, let "x" be the distance between the man and the post, and let "s" be the other part.

 

Using similar triangle, you will get a proportion of: s/7 = (s+x)/20

 

Using a magic math solving machine, you can solve for the value of "s" in terms of "x", s = (7/13)*x

 

We solved for s because that's the rate in question or ds/dt. To get ds/dt, we differentiate the equation by d/dt.

 

We will get: (ds/dt) = (7/13)(dx/dt), which as you can observe is just constant rates, and that's ok because they're really just proportional.

 

dx/dt is actually the 5 ft/s, substituting that, you will get (ds/dt) = 35/13 ft/s, that is my answer but this solution made the 16 ft useless.

 

*16 ft will be useful if the question is about the rate somewhere in the hypotenuses, be it the big one or the small one.