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|= √(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.