Hello, stud_02!

Wow! . . . What a long, intricate problem!

Code:

A
* - -
| : :
| : 16gtē
| : :
* B : -
* | : :
* | ―gTē :
D * | : :
o y | : 16gTē-16gtē
* | | : :
* |gTt | : :
* | | : :
o-----------*-----------* - -
S x-a E a C
: - - - - - x - - - - - :

The tower is:

In seconds, the light falls: feet.

Hence: .

The stone is thrown upward from feet.

We have:

The shadow of the stone is at

. . Then:

We have similar right triangles: .

So we have: .

Substitute [1]: .

. . and we have: .

Differentiate: .

. . which simplifies to: .

Now plug in

But check my work . . .*please!*

.