Position Vector & Displacement: Particle Homework

[tjbateh]

Homework Statement

A watermelon seed has the following coordinates: x = -8.1 m, y = 8.8 m, and z = 0 m. Find its position vector as (a) a magnitude and (b) an angle relative to the positive direction of the x axis. If the seed is moved to the xyz coordinates (3.3 m, 0 m, 0 m), what is its displacement as (c) a magnitude and (d) an angle relative to the positive direction of the x axis?

Homework Equations

The Attempt at a Solution

a= 11.9 Meters
b= 133 degrees
c= 15.2 Meters
d = ?

How do I find this final angle??

 

[kuruman]

Find the x and y components of the displacement vector and get the angle the usual way.

 

[tjbateh]

All I have is the magnitude of the displacement vector. I know I need to find the x and y components of it, but how do I do that without at least having one of the angles? Or do i already have it??

 

[kuruman]

You have the coordinates of two points. The displacement is a vector whose components is the difference finish - start, (x₂-x₁, y₂-y₁, z₂-z₁)

 

[tjbateh]

so my displacement vector's components are (11.4, -8.8, 0)? So the angle would be inverse tan of (-8.8/11.4)?

 

[kuruman]

Correct.

 

[tjbateh]

the angle I get from that calculation is -37.67..Now it says it wants an angle relative to the positive direction of the x-axis. Would that be it, or do I have to subtract that number from something else?

 

[kuruman]

Draw the point on a sheet of paper. Connect it with a straight line to the origin. Then look at the angle that starts on the positive x-axis and goes counterclockwise to the line that you have drawn. That's the one you want. What is its relation to 37.67 degrees?

 

[tjbateh]

ok, is it 360-37.67? which is going to be 322.33

 

[tjbateh]

I put in 322.33, and it came out wrong! The correct angle was -37.67..Bummer

 

[kuruman]

Bummer indeed. If this is one of those evil Web-based, calculated type questions like Webassign or Mastering Physics, I think you should explain your answer to your instructor. Chances are he/she will override the machine. I know I would.

 

[tjbateh]

yea wiley plus..Horrible system!

 

[tjbateh]

thanks anyways for your help!