Chapter 3, Problem 3Q

Being part of the “Gators,” the University of Florida golfing team must play on a putting green with an alligator pit. Figure 3-22 shows an overhead view of one putting challenge of the team; an xy coordinate system is superimposed. Team members must putt from the origin to the hole, which is at xy coordinates (8 m, 12 m). Hut they can putt the golf Hall using only one or more of the following displacements, one or more times:

Figure 3-22 Question 3.

${\stackrel{\to }{d}}_{\text{1}}=\text{(8 m) <mover accent="true"> i <mo> ^ </mo> </mover> + (6 m) <mover accent="true"> j <mo> ^ </mo> </mover>, }{\stackrel{\to }{d}}_{\text{2}}\text{=(6 m) <mover accent="true"> j <mo> ^ </mo> </mover>, }{\stackrel{\to }{d}}_{\text{3}}\text{ = (8 m) <mover accent="true"> i <mo> ^ </mo> </mover>}\text{.}$

The pit is at coordinates (8 m, 6 m). If a team member putts the ball into or through the pit, the member is automatically transferred to Florida State University, the arch rival. What sequence of displacements should a team member use to avoid the pit and the school transfer?