Displacement and Vectors

In summary, the expert golfer could make the hole in what single displacement if they started at the same initial point as the novice and took the first movement of the ball, which was 4.00 m to the north.
  • #1
Monis
4
0

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]
 
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  • #2
Monis said:

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.
 
  • #3
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
 
  • #4
Monis said:
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:

compass-rose-27817649.jpg

 
  • #5
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=
 
  • #6
Monis said:
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.
 
  • #7
Thank you so much for the help, I understand it much better now !
 

1. What is displacement?

Displacement is a measure of the change in position of an object. It is a vector quantity, meaning it has both magnitude (size) and direction.

2. How is displacement different from distance?

Displacement is a specific type of distance measurement that considers the initial and final positions of an object, while distance is a measurement of the total length traveled by an object, regardless of direction.

3. What is a vector?

A vector is a quantity that has both magnitude and direction. It is often represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

4. How are vectors typically represented?

Vectors are typically represented using coordinates, such as x and y values on a graph, or by using mathematical notation, such as vector A = (3, 5).

5. How do you calculate the resultant vector?

To calculate the resultant vector, you must first determine the individual components (x and y values) of each vector. Then, add the x components together and the y components together to get the resultant vector's x and y values. Finally, use the Pythagorean theorem to find the magnitude and trigonometry to find the direction of the resultant vector.

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