Birdman is flying horizontally at a speed of 40 m/s and a height of 58
m. Birdman releases a turd directly
above the start of the field. How far
from the start of the field should the
robot hold the bucket to catch the
turd?

The robot should hold the bucket at 137.6 m from the start of the field

Explanation:

Horizontal Motion

When an object is launched horizontally with a speed v from a height h, it describes a curved path exclusively ruled by gravity until it eventually hits the ground.

The range or maximum horizontal distance d traveled by the object can be calculated as follows:

Birdman flies horizontally at a  speed of v=40 m/s and a height of h=58  m. He releases a turd above the start of the field. If the robot was exactly down  Birdman, then it won't catch the turd with the bucket because it would land farther away by a distance equal to the range. Thus:

d = 137.6 m

The robot should hold the bucket at 137.6 m from the start of the field