<p>Here's a related rates problem that just completely stumped me.</p>
<p>A 6 foot tall man is walking away from a 24 foot tall street light. How fast is his shadow lengthening when he is sqrt(5e)/pi feet away from the light?</p>
<p>You need to draw a good picture.
(mine sucks, but MAYBE you can get the idea)
.|...\
2|....\
4|.....|\
f|...6 |..\
t|...f |... \
.|...t |..... \
.|<strong><em>|</em></strong>__\
x........y
x=sqrt(5e)/pi
his shadow is given by y - so we want dy/dt
The point is that there are two similar right triangles. The big one is formed by the 24ft light and the small one by the 6ft man.</p>
<p>Umm... i just read the question again and you're missing a piece of data - the man's speed. His shadow would be lengthening at a diffrent rate depending on if he's sprinting or walking or stopped.</p>
<p>Whatever:
y/6=(x+y)/24
cross multiply and simplify: x=3y
dx/dt = 3dy/dt
dy/dt = 1/3 dx/dt</p>
<p>This seems a little too simple, but i think it is right. You just need to plug in the given that you didn't post, and (apparently) the distance from the light doesn't matter... Maybe i made an error though.</p>
<p>whoops! the man is walking at 4 ft/sec.</p>
<p>Well, then he's not walking, he's power walking.</p>
<p>the the answer is 4/3 ft/s i guess :)</p>