A tightrope is stretched 30 feet above the ground between two buildings which are 50 feet apart.
A tightrope walker, walking at a constant rate or 2 ft/ sec from point A to point B,
is illuminated by a spotlight 70 feet above point A.
How fast is the shadow of the tightrope walker's feet moving along the ground
when she is midway between the buildings?
I am so confused. Where do I start? . . . . Make a sketch!
70 | *
| * T
A * - - - - - o - - - - - - * B
| x * |
30 | * | 30
| * |
* - - - - - - - - - o - - *
C - - - - s - - - - E D
: - - - - - -50 - - - - - :
The tightrope walker is at , having walked feet from to
The spotlight is at , casting the shadow at on the ground.
From similar right triangles, we have: .
Differentiate with respect to time: .
Since ft/sec: . ft/sec.