Hello, math619!

A light is on the ground, 15 m from a wall.

A woman, 1.6 m tall, walks away from the light and towards the wall at 0.5 m/s.

Calculate the rate of change of the length of her shadow on the wall

when the woman is 10 m from the wall.

I guess you would have to find the rate at which the tip of her shadow is moving.

. . Right! Code:

*
* |
* |
* |
* | s
* | |
* |1.6 |
* x | |
*-----------+-----------*
: - - - - 15 - - - - - :

From similar right triangles, we have: .

. . and we have: .

Differentiate with respect to time: .

We are given: . . . . and "10 m from the wall" means

. . Therefore: .