Shadow cast by a curved wall
- Author:
- Elliot Malkin
A wall follows the path of for .
The wall has height where is the curved distance along the wall from and and are constants.
The sun is due South of this setup, at an angle of from vertical (its "zenith angle").
The sun causes the wall to cast a shadow.
Question: what curve must the wall follow so that the full extent of its shadow is at a constant perpendicular distance from the wall?
The image shows the plan view of the wall following . The pink curve remains at a constant distance from the wall. The grey curve follows the extent of the wall's shadow. So the question becomes:
What function causes the pink curve and the grey curve to coincide?
(Here's the same question on Stackexchange .)