The physics
The lamp, your head and your shadow's tip lie on one straight ray. That makes two similar triangles. The big one has the lamp's height H. The small one has your height h.
xtip = x · H / (H − h) L = x · h / (H − h)
Distances in a fixed ratio mean speeds in the same ratio. So the tip moves at a steady v H / (H − h), faster than you. The shadow grows at a steady v h / (H − h).
Now throw a ball flat from the lamp's own spot. Its shadow falls on a wall D away. The ray's slope is (½ g t²) / (u t) = g t / (2u). So the shadow slides down the wall at a steady g D / (2u).