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Components of unit vectors

  • Thread starter roam
  • Start date
  • #1
1,266
11

Homework Statement



A golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East and the third 5.7 m South-West.

Express each of these three displacements in unit vector notation where i is a unit vector pointing due East and j is a unit vector pointing due North.

E.g the first displacement is: [tex](0)i, (2.5)j[/tex]

The Attempt at a Solution



The first one is obvious but the other two aren't. For example for the second part the question says it is 4.8 m South-East BUT it doesn't say how many degrees due South-East. Without the angle, it is impossible for me to find the rectangular components (i.e [tex]4.8 sin(\theta), 4.8 cos(\theta)[/tex]). Any suggestions?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
7
When they say south of east or south of west the angle is always 45 degrees with east-west line.
 
  • #3
1,266
11
Oh thanks! I found the three displacements in unit vector notation:

[tex]0i, 2.5j[/tex]
[tex]3.39i, -3.39j[/tex]
[tex]-4.03i, -4.03j[/tex]

The question then asks:

Determine the angle in degrees (measured with respect to anticlockwise rotation from an axis pointing due East of the hole) to get the ball into the hole in a single putt.

What do I need to do to answer this problem? I'm a little confused...
 
  • #4
rl.bhat
Homework Helper
4,433
7
Find the resultant of these three vectors.
Then tanθ = y/x
 

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