Vector displacement problem trouble

[M1ZeN]

Homework Statement

While vacationing in the mountains, you do some hiking. In the morning, your displacement is S-morning = (1600 m, east) + (3300 m, north) + (160 m, vertical). After lunch your displacement is S-afternoon = (1800 m, west) + (2000 m, north) - (350 m, vertical). At the end of the day, how much higher or lower (in m) are compared to your starting point in the morning?

Homework Equations

A^2 + B^2 = C^2

The Attempt at a Solution

I can't find any other relevant equations that is in the chapter and no examples are given with a third displacement value.

My attempt in the problem using the same method for both the morning values and after lunch values:

(1600)^2 + (3300)^2 = C^2
c = 3667.4 m

then...

(3667.4)^2 + (160)^2 = C^2
c = 3670.9 m

I used the same method for the afternoon values, found the difference between the two (1003.1 m), and it was the incorrect answer.

Thanks,
Daniel

 

[rl.bhat]

In the morning, how much up you go?
In the afternoon, from the above point how much down you go?
So what is the final depth from the starting point?
The other distances are just distractions.

 

[Slacker142]

Homework Statement

While vacationing in the mountains, you do some hiking. In the morning, your displacement is S-morning = (1600 m, east) + (3300 m, north) + (160 m, vertical). After lunch your displacement is S-afternoon = (1800 m, west) + (2000 m, north) - (350 m, vertical). At the end of the day, how much higher or lower (in m) are compared to your starting point in the morning?

Homework Equations

A^2 + B^2 = C^2

The Attempt at a Solution

I can't find any other relevant equations that is in the chapter and no examples are given with a third displacement value.

My attempt in the problem using the same method for both the morning values and after lunch values:

(1600)^2 + (3300)^2 = C^2
c = 3667.4 m

then...

(3667.4)^2 + (160)^2 = C^2
c = 3670.9 m

I used the same method for the afternoon values, found the difference between the two (1003.1 m), and it was the incorrect answer.

Thanks,
Daniel

Daniel I think you are misreading the problem, they ask for the change in altitude from your starting point. Assuming that is 0m you just need to add or subtract the vertical distances they give you using say 0m as your starting point.

Since they give you the changes in vector form you can call the last piece the z axis or K-hat values of the vector and ignore the other dimensions.

Hope that helps

If it doesn't then this should be your answer

Spoiler

0+ 160m - 350m = -190m so your ending altitude would be 190 m less then your starting point

 

[M1ZeN]

I found the correct answer for that part. Now the second part has asked me to: What is the magnitude of your net displacement (in km) for the day?

I went back to the method I used and just added the separate values for both morning and afternoon. It was the incorrect answer but I figured what I did was reasonable enough to try to find an answer.

 

[rl.bhat]

Project every displacement on the single plane, then find the net x, y component. z component is known. Find net displacement.