Bird Watcher's Displacement and Velocity

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SUMMARY

The discussion focuses on calculating the displacement and average velocity of a bird watcher who walks 0.45 km due east, 0.70 km due south, and 2.75 km at an angle of 43.0° north of west over a duration of 2.50 hours. The correct approach involves determining the x and y components of each leg of the journey, with the final displacement calculated using the Pythagorean theorem. The average velocity is derived by dividing the total displacement by the total time.

PREREQUISITES
  • Understanding of vector components and trigonometry
  • Familiarity with the Pythagorean theorem
  • Knowledge of basic kinematics
  • Ability to interpret angles in vector problems
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  • Calculate the x and y components of the bird watcher's total displacement
  • Apply the Pythagorean theorem to find the magnitude of the displacement
  • Determine the average velocity using the total displacement and time
  • Explore vector addition techniques for more complex motion scenarios
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Students studying physics, particularly those focusing on kinematics and vector analysis, as well as educators seeking to clarify vector component methods.

scw287
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A bird watcher meanders through the woods, walking 0.45 km due east, 0.70 km due south, and 2.75 km in a direction 43.0° north of west. The time required for this trip is 2.50 h.
(a) Determine the magnitude and direction (relative to due west) of the bird watcher's displacement. Use kilometers and hours for distance and time, respectively.
(b) Determine the magnitude and direction (relative to due west) of the bird watcher's average velocity.

Heres what I have done so far:

X component=.45+2.7cos43=-2.425
Y component=.70+2.7sin43=-2.541

2.7/2.5=1.08
square root of (-2.425^2)+(-2.541)^2=3.512<<<<... answer is wrong

I also tried using trig tan-1(2.425/2.541)


OR WOULD it be 2.7cos43-.45 & 2.7sin43-.70
 
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scw287 said:
Heres what I have done so far:

X component=.45+2.7cos43=-2.425
Y component=.70+2.7sin43=-2.541
Get your signs straight. Pick +X to be East and +Y to be North. (When you're done you can reword the answer with respect to due West, like they want it.) Redo this.

Did you draw out the path taken? That will help keep your signs in line.
 
Doc Al said:
Get your signs straight. Pick +X to be East and +Y to be North. (When you're done you can reword the answer with respect to due West, like they want it.) Redo this.

Did you draw out the path taken? That will help keep your signs in line.

yes it would be a right triangle, I think. So I would have .45*sin43<x component and -.70*cos43<y component and I have 2.75 for the hypoteneuse. Also I know the total time was 2.5 hrs. so I'm guessing I need to use a kinematics equation to solve for x?
 
The path is not a right triangle. To find the x-component of the displacement, just add the x-component for each of the three "legs" of his path. Do the same for the y-component.

Show the components you get for each leg including the correct sign.
 
Doc Al said:
The path is not a right triangle. To find the x-component of the displacement, just add the x-component for each of the three "legs" of his path. Do the same for the y-component.

Show the components you get for each leg including the correct sign.

This is where I struggle is the component method: would it be .45sin43+0=.307 & -.70cos43+0=-.512 Then would I take the square root of (.307^2)+(-.512^2)
or do I do it like this: .45sin43+-.70cos43+2.75cos43=1.806
 
Let's start over. Do this: Find the x & y components of the displacement for each of the three "legs" of the path.
scw287 said:
A bird watcher meanders through the woods, walking 0.45 km due east, 0.70 km due south, and 2.75 km in a direction 43.0° north of west.
Do it systematically, step by step.
 
Thats what I've been trying to do, my teacher hasn't spent very much time on these problems and i barely understand the component method
 
You'll understand it better once you try to solve the problem. Do the first step right now: 0.45 km due east

What's the x-component of the displacement?
What's the y-component of the displacement?

(Draw the step on a diagram!)
 
This might help: http://id.mind.net/~zona/mstm/physics/mechanics/vectors/componentAddition/componentAddition2.htm"
 
Last edited by a moderator:
  • #10
x-comp: .307
y-comp:-.512
 
  • #11
scw287 said:
x-comp: .307
y-comp:-.512
No. How did you get those numbers? The motion is due east, which means completely in the +X direction.

Did you draw a diagram?

The only time angles are involved (for calculating components) is when the vector makes some angle with the x-axis.
 
  • #12
yes I drew a diagram, I just thought that if you had an angle i would have to find the x and y components using the component method...I got the .307 and /.512 using the vector length X cos or sin of the angle measure.
 
  • #13
Draw a diagram just for the first step. 0.45 km due east

The diagram should just be an arrow pointing to the right (+x direction). No angles needed.
 
  • #14
okay I've got that...then I should have an arrow pointing downward due south from the end of the previous vector? then i drew an arrow from the end of that vector 43 degrees north of west
 
  • #15
scw287 said:
okay I've got that...then I should have an arrow pointing downward due south from the end of the previous vector? then i drew an arrow from the end of that vector 43 degrees north of west
Yes, but draw each step separately so you can find the components. Then just add the x-components together to find the x-component of the total displacement. Same thing for the y-components.
 
  • #16
0.45 km + 0.70 km + and 2.75 km=3.9 km
 
  • #17
scw287 said:
0.45 km + 0.70 km + and 2.75 km=3.9 km
If you're adding x-components, only the first term is correct.

If something goes due south, what's its x-component?
 
  • #18
.45<x-component so y=0
if something goes due south its x-component=0 so it would be just -.70
 
  • #19
OK, but be careful not to add x- & y-components together: keep them separate. Add up all the x-components to get the x-component of the total; then do a similar, but separate, calculation for the y-component.
 
  • #20
isn't there only one x-component so it would =.45
and one y component=.70<<these answers seem too obvious am I missing something?
 
  • #21
scw287 said:
isn't there only one x-component so it would =.45
and one y component=.70<<these answers seem too obvious am I missing something?
You're missing the last step in the path, the one that's at an angle. That step will have a non-zero x- and y-component.
 
  • #22
o, okay so 2.7*cos43-x comp 2.7*sin43-y
 
  • #23
i feel retarded that i don't understand this problem I've had the most problems with vectors than any other concept so far
 
  • #24
scw287 said:
o, okay so 2.7*cos43-x comp 2.7*sin43-y
Careful with signs. The direction is 43.0° north of west, which means:
x-comp = -2.75*cos43
y-comp = 2.75*sin43

Note: The given step is 2.75km, not 2.7km.
 
Last edited:
  • #25
i got you so now i need to find the magnitude and i use pythagorean theorem right?
 
  • #26
i haave exactly 4 mins to figure this out I've been working on this for hours please help
 
  • #27
scw287 said:
i got you so now i need to find the magnitude and i use pythagorean theorem right?
Right. First find the x and y components of the total displacement.
 
  • #28
2.425 2.541
 
  • #29
scw287 said:
2.425 2.541
How did you get these numbers?
 

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