Hello, qu2010!

1. A spotlight is on the ground 100 feet from a vertical building.

A 6-foot man starts at the spotlight and walks towards the building at 5 ft/sec. Code:

C *
| * A
| *
y | | *
| |6 *
| | *
* - - - * - - - - - - - * - -
D x B 100-x L
: - - - - 100 - - - - - :

The spotlight is at

The man is: .

His shadow is: .

His distance from the building is: .

. . Hence: .

We are given: . ft/sec.

From similar right triangles

. . Then: .

Differentiate with respect to time: .

. . and we have: .

a) How fast is the top of the man's shadow moving down the building

when he is 50 feet from the building? When . . .

. .

b) How fast is the top of the man's shadow moving down the building

when he is 25 feet from the building? When . . .

. .