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: .