wouldn't it be
15 / 8 ---> 15y - 15 x = 8y
solving for y
y = 15/7

so would'nt it be
15/7 (8)

where am I going wrong

wait or would I be solving for y which is 15y - 15x = 6y because of his height instead of the feet per second his walking?

dont u gotta set up 2 constant acceleration equations for X and Y directions and set it equal to eac other?

First, notice that the answers doesn't depend on the position from the base (10 feet in your case).

Intercept theorem (Thales' theorem) proves that the length of the shadow equals 8/7 of the position from the base.
If the position from the base changes at a rate of 8 feet/sec, the length of the shadow changes at a rate of (8/7)*8 = 64/7 feet/sec.

The distance between the tip of the shadow and the base of the light equals the length of the shadow plus the distance between the man and the base of the light.
The velocity of the tip, hence, is the sum of the velocity of the man and the velocity of the length of the shadow :
8 feet/sec + 67/7 feet/sec = 120/7 feet/sec.

for part a

• 1 Express the position of the tip of the shadow as a function of time
• 2 Take the derivative of this function with respect to time
• 3 Figure out how long the man was walking (get a value of time)
• 4 substitute this into the derivative

1) P(t) is position of the tip of the shadow, also the length of the base of the big triangle
similar triangles:
(9)/(8t) = 15/[P(t)]
P(t) = (40*t)/3

2)dP/dt = 40/3 f/s
We can skip step 3 and 4 since time disappeared from our equation (preforming step 3 and 4 won't change our answer, since there is no t to replace).

This post was edited by Azrad on Sep 28 2013 02:36pm

for part b:


clearly:
dP/dt = da/dt + db/dt
We know dP/dt is a constant (40/3 f/s), and we know da/dt is a constant (8 m/s), therefore db/dt had also better be a constant so we can just use simple algebra for it:

40/3 = 8 + db/dt
db/dt = 16/3 f/s

I had a 8 feet heigth man in mind... sorry for this confusing post.

Azrad' explanations are correct.

heh yeah your description sounded good but i couldn't follow your work (and now we know why)
Also I couldn't see ahead that the solution was not a function of time---I would have guessed otherwise---but can't argue with the results.

This post was edited by Azrad on Sep 28 2013 03:22pm

Yeah I got it! That was the mistake I made with the 8 feet being height haha
Thanks Azrad for the explanation