Thread: Related Rate models question

I'm getting the biggest headache trying to solve this question.. and its probably the easiest question ever but I just can't get the right answer and its driving me nuts. And i have a test on monday on this stuff.. so any help would be appreciated beyond belief.

A man 2 m tall walks away from a lamppost whose light is 5 m above the ground. If he walks at a speed of 1.5 m/s, at what rate is his shadow increasing when he is 10 m from the lamppost.

The answer is supposed to be 1 m/s, but I keep on getting 2.5 m/s, and I have no clue what I'm doing wrong.

Thanks for the help!!!

Let x=shadow length and y=distance bewtween man and lamppost.

Similar triangles:





Differentiate:



We know that dy/dt=3/2

We have:

Hello, jmailloux!

A man 2 m tall walks away from a lamppost whose light is 5 m above the ground.
If he walks at a speed of 1.5 m/s, at what rate is his shadow increasing
when he is 10 m from the lamppost.

The answer is supposed to be 1 m/s, but I keep on getting 2.5 m/s,
and I have no clue what I'm doing wrong. . I know!

You made a very common error.
I know ... I still do it from time to time.

Code:

      *
      |   *
      |       *
      |           *
     5|           |   *
      |          2|       *
      |           |           *
      * - - - - - + - - - - - - - *
      :     x     :       s       :

I bet you let equal the whole bottom of the diagram.
That would give us the rate at which the tip of his shadow is moving.
. . But they want the rate at which the length of his shadow is changing.

From the similar right triangles, we have: .

Then: .

Differentiate with respect to time: .


The man's speed is 1.5 m/sec: .

Therefore: .

thank you soo much

it makes a lot more sense after you explained it, and i did make s equal to the whole bottom of the diagram.

anyways.. thanks for the help!