# Help with Displacement ( Vectors)

• ipwnj00
In summary, the conversation discusses a hiker's travel in different directions and attempts to find the resulting displacement. The hiker travels 3.2 km at 42 degrees north of west, 2.1 km at 12 degrees west of south, and 1.9 km at 62 degrees east of north. The resulting displacement is calculated using trigonometric functions, but the correct solution is achieved by using the coordinates of West and North as positive and East and South as negative.
ipwnj00

## Homework Statement

A Hiker travels in the following directions
i) 3.2 Km ( N 42 W)
ii) 2.1 Km ( W 12 S )
iii) 1.9 Km ( E 62 N)

A) what is the resulting displacement?

## The Attempt at a Solution

A)
X Dir

3.2 sin 42 = 2.14
2.1 cos 12 = 2.05
1.9 cos 62 = .89
total = .94 <<<<<, Total is wrong :(
Y Dir

3.2 Cos 42 = 2.38
2.1 sin 12 = .44
1.9 sin 62 = 1.68
.26 <<< Total is wrong too

Can anyone explain on the X and Y Directions, Like where to Use positive and Negative Sign. I really Need help with this :P Beacuse it confuses me that were should i use the signs other than that rest is perfect.

Thanks for the help In Advance ^.^

Welcome to PF.

The way I do it is draw a diagram.

I set N as positive Y and East as positive X.

Then I use that to keep track of the sign.

The N 42 W I read in quadrant notation in this regime then as +Y, -X with the angle made with the vertical Y axis.

Fwiw, I think quadrant notation usually uses just N or S followed by angle or direction E or W. For some reason this problem is using E and W as well, but I still read it as Direction - angle - direction off that direction.

I would assume that the problem is using this convention as well, unless you have previous experience with the conventions used in your course work.

thanks for the help, but ... i used it like u said still wrong... I have the answer key with me so yeah here's the problem aagain :

3.2 sin 42 = +2.14
2.1 cos 12 = -2.05
1.9 cos 62 = +.89
total = .94 <<<<<, Total is wrong :(
Y Dir

3.2 Cos 42 = - 2.38
2.1 sin 12 = -.44
1.9 sin 62 = +1.68
.26 <<< Total is wrong tooHEre's the Answer key i have it with me :P

3.2 sin 42 = +2.14
2.1 cos 12 = +2.05
1.9 cos 62 = -.89
total = 3.304
Y Dir

3.2 Cos 42 = + 2.38
2.1 sin 12 = - .44
1.9 sin 62 = +1.68
Total ==== 3.62

Meh can u Look again xD if u need more details i'll scan and post it on the web :P

It looks like that would be the problem.

When they say N 42 W, they are meaning 42 N of West

It seems they chose West as positive too.

Draw it out carefully, only reading it as:
North 42 degrees from West
West 12 degrees from South.
East 62 degrees from North.

I think that yields the right answer.

To answer your original question so long as you are consistent in staying with whatever sign you choose for your coordinates you should get to the same result.

However understanding their notation is also key.

Good Luck.

ok thanks :P btw my exam on physics is next week so i was having some trouble with that :P

## 1. What is displacement?

Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position. It is represented by a directed line segment and is measured in units of distance, such as meters or feet.

## 2. How is displacement different from distance?

Distance is a scalar quantity that measures the total length of the path traveled by an object. Displacement, on the other hand, is a vector quantity that only considers the change in position and does not take into account the path taken.

## 3. How do you calculate displacement?

Displacement can be calculated by subtracting the initial position vector from the final position vector. It can also be calculated by using the Pythagorean theorem for two-dimensional displacement or by using the scalar product for three-dimensional displacement.

## 4. What is the difference between displacement and velocity?

Displacement is a vector quantity that measures the change in position of an object, while velocity is a vector quantity that measures the change in displacement over time. In other words, velocity takes into account the direction and speed of an object's motion, while displacement only considers the change in position.

## 5. How is displacement used in real life?

Displacement is used in various real-life situations, such as navigation, sports, and transportation. It can also be used in calculating the work done by a force and in determining the position of an object at a specific time. In engineering, displacement is an important factor in designing structures and machines.

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