Question

During his first golf tournament (at age 2), tiger woods actually had to four-putt one of the holes (meaning he had to putt the ball four times before it went in!). his putts were as follows: 10 meters southwest, 3 meters north, 4 meters southeast, and 0.5 meters west. how far was the hole from his original putting position? in what direction?

Answer 1

(xy) Chartesian cooredinates system. Positive x towards East, positive y towards North $i, j \rightarrow$ unit vectors on $x,y$
10 meters Southwest is $r_1 =-10*cos 45 *i -10*sin 45*j =(-7.07*i-7.07*j) (m)$
 3 meters North is $r_2=3j (m)$
4 meters Southeast is $r_3 =4*cos 45*i-4*sin45*j=2.83*i-2.83*j (m)$
0.5 meters West is $r_4 =-0.5*i (m)$

Total displacement is $r=r_1 +r_2+r_3+r_4=(-7.07i-7.07j)+3j+(2.83i-2.83j)-0.5i$
$r= -4.74i-6.90j (m)$
$|r|= \sqrt{4.74^2+6.90^2}=8.37 (m)$
Direction is
$\tan \alpha =y/x=6.90/4.74=1.456$
Thus $\alpha =55.51 (degree)$ counterclockwise from x axis.