Answer:
The parabolic shape of the door is represented by . (See attachment included below). Head must 15.652 inches away from the edge of the door.
Step-by-step explanation:
A parabola is represented by the following mathematical expression:
Where:
- Horizontal component of the vertix, measured in inches.
- Vertical component of the vertix, measured in inches.
- Parabola constant, dimensionless. (Where vertix is an absolute maximum when
or an absolute minimum when
)
For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:
(Vertix)
(x-Intercept)
(x-Intercept)
The following equation are constructed from the definition of a parabola:
The parabolic shape of the door is represented by . Now, the representation of the equation is included below as attachment.
At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:
If y = 22 inches, then x is:
Head must 15.652 inches away from the edge of the door.
