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.
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: .
Differentiate with respect to time: .
The man's speed is 1.5 m/sec: .