1. ## Another Optimization Question

hello, I posted an optimization question earlier and I got another one that I am struggling with. It states:

A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Is the length of his shadow on the building increasing or decreasing? Find the rate of change of the length of his shadow when he is 4 m from the light.

Any help will be greatly appreciated!

thanks a lot!

2. Originally Posted by dmitri
hello, I posted an optimization question earlier and I got another one that I am struggling with. It states:

A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Is the length of his shadow on the building increasing or decreasing? Find the rate of change of the length of his shadow when he is 4 m from the light.

Any help will be greatly appreciated!

thanks a lot!
Why don't you post your work as of now? Here is a hint, this will involve similar triangles.

3. Use similar triangles. Draw a diagram.

$\frac{y}{15}=\frac{2}{x}$

$y=\frac{30}{x}$

Now, differentiate both sides wrt time, enter in your givens and you're done.