Chapter 12.5, Problem 12.8PP

A.

Explanation of Solution

Determining trajectories:

The given trajectories is the safe trajectories.

• A trajectory that pass the edge of unsafe region is called “safe trajectory”.
• The given trajectory “${\text{H}}_{\text{1}}{\text{, L}}_{\text{1}}{\text{, U}}_{\text{1}}{\text{, S}}_{\text{1}}{\text{, H}}_{\text{2}}{\text{, L}}_{\text{2}}{\text{, U}}_{\text{2}}{\text{, S}}_{}$

B.

Explanation of Solution

Determining trajectories:

The given trajectories is the unsafe trajectories.

• A trajectory that touches the unsafe region is called “unsafe trajectory”.
• The given trajectory “${\text{H}}_{\text{2}}\text{,}{\text{L}}_{\text{2}}\text{,}{\text{H}}_{\text{1}}\text{,}{\text{L}}_{\text{1}}\text{,}{\text{U}}_{\text{1}}\text{,}{\text{S}}_{\text{1}}\text{,}{\text{T}}_{\text{1}}\text{,}\text{\hspace{0.17em}<}$

C.

Explanation of Solution

Determining trajectories:

The given trajectories is the safe trajectories.

• A trajectory that pass the edge of unsafe region is called “safe trajectory”.
• The given trajectory “${\text{H}}_{\text{1}}{\text{, H}}_{\text{2}}{\text{, L}}_{\text{2}}{\text{, U}}_{\text{2}}{\text{, S}}_{\text{2}}{\text{, L}}_{\text{1}}{\text{, U}}_{\text{1}}{\text{, S}}_{\text{1}}\text{,}{\text{T}}_{\text{1}}{\text{, T}}_{\text{2}}$” pass the edge of unsafe region is shown below