1. ## related rates

A man 6 ft tall walks at the rate of 5 ft/ sectoward a streetlight that is 16 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?

2. Did you leave out details about the light? And are the "particle" and the "man" the same thing?

3. oops, sorry......i mixed two different problems........

4. Originally Posted by turtle

A man 6 ft tall walks at the rate of 5 ft/ sectoward a streetlight that is 16 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?
x'(t)=-5ft/s
Draw a right triangle base s+x, height 16 where s is the length of the shadow and x is the distance from the light.

You can see that (s+x)/16=s/6
Solve for x to get x=5s/3
Implicitly differentiate both sides x'=5s'/3
Solve for s'(t)=3x'(t)/5
Plug x'(t)=-5 to get s'(t)=-3ft/s

(I think this is right but I haven't done this in a few years so this is my disclaimer. Wait for someone to confirm if you want to be sure.)

5. Originally Posted by splash
x'(t)=-5ft/s
Draw a right triangle base s+x, height 16 where s is the length of the shadow and x is the distance from the light.

You can see that (s+x)/16=s/6
Solve for x to get x=5s/3
Implicitly differentiate both sides x'=5s'/3
Solve for s'(t)=3x'(t)/5
Plug x'(t)=-5 to get s'(t)=-3ft/s

(I think this is right but I haven't done this in a few years so this is my disclaimer. Wait for someone to confirm if you want to be sure.)
Looks good to me!

-Dan