What is the single displacement needed for an expert golfer to make the hole?

[Monis]

Homework Statement

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0° west of south (Fig. P3.21). Starting at the same initial point, an expert golfer could make the hole in what single displacement?

Homework Equations

R= A+B
R=Sqrt(Rx2+Ry2)

The Attempt at a Solution

I tried adding all the displacements together and trying to get a value. But I'm confused as to what to do with the angle that is provided.[/B]

 

[SteamKing]

Homework Statement

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0° west of south (Fig. P3.21). Starting at the same initial point, an expert golfer could make the hole in what single displacement?

Homework Equations

R= A+B
R=Sqrt(Rx2+Ry2)

The Attempt at a Solution

I tried adding all the displacements together and trying to get a value. But I'm confused as to what to do with the angle that is provided.[/B]

Show your calculations.

If you know how to express a vector in terms of its components, this problem should be easy to solve.

 

[Monis]

I tried putting the components together like this
4cos0= 4i
4sin0= 0j
2cos90=0i
2sin90= 2j
1cos30= .86
-1cos30= -0.5

Then I added all the components of (i) and got 4.86i
added all the components of (j) and got 1.5j
used Pythagorean theorem and got an answer of 5.086

 

[SteamKing]

I tried putting the components together like this
4cos0= 4i
4sin0= 0j
2cos90=0i
2sin90= 2j
1cos30= .86
-1cos30= -0.5

Then I added all the components of (i) and got 4.86i
added all the components of (j) and got 1.5j
used Pythagorean theorem and got an answer of 5.086

You need to make a sketch.

Take the first movement of the ball, which is 4.00 m to the north. How would you show north on your sketch?
Second movement, 2.00 m to the northeast. Which direction is northeast? Is northeast at right angles to north?

If you are having trouble visualizing a compass, here is a sketch of one:

​

 

[Monis]

So if I'm not given a specific angle I should assume that whatever the direction is that's what the angle is? e.g northeast points to a 45º angle
so i would do
2cos45=
2sin45=

 

[SteamKing]

So if I'm not given a specific angle I should assume that whatever the direction is that's what the angle is? e.g northeast points to a 45º angle
so i would do
2cos45=
2sin45=

Yes.

Directions are equivalent to angles; you just have to know how to read a compass.

There are certain cardinal compass directions, like north, south, east, and west, which are pretty obvious. There are also some intermediate compass directions, like northeast, etc., which are also common. For less common compass directions, you have expressions like "30.0° west of south", which describes the heading to take.

 

[Monis]

Thank you so much for the help, I understand it much better now !