Bird Watcher's Displacement and Velocity

In summary: Same thing for the y-components.0.45 km-0.70 km- and 2.75 km=2.35 km0.45 km-0.70 km- and 2.75 km=2.35 km
  • #1
scw287
51
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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
 
  • #6
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.
 
  • #7
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
 
  • #8
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!)
 
  • #9
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.
 
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  • #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?
 

FAQ: Bird Watcher's Displacement and Velocity

What is Bird Watcher's Displacement?

Bird Watcher's Displacement is the distance between the starting point and the current location of a bird. It is usually measured in meters or kilometers, depending on the scale of observation.

How is Bird Watcher's Displacement calculated?

To calculate Bird Watcher's Displacement, you need to know the starting point and the current location of the bird. You can then use the distance formula, which is D = √[(x2-x1)^2 + (y2-y1)^2], where x1 and y1 are the coordinates of the starting point and x2 and y2 are the coordinates of the current location.

What is the difference between Bird Watcher's Displacement and Velocity?

Bird Watcher's Displacement is a measure of the distance traveled by the bird, while Velocity is a measure of the displacement over a period of time. In other words, Displacement is a scalar quantity, while Velocity is a vector quantity that includes direction and magnitude.

How is Bird Watcher's Velocity calculated?

To calculate Bird Watcher's Velocity, you need to know the displacement and the time taken for the bird to travel that distance. The formula for Velocity is V = D/t, where V is the Velocity, D is the Displacement, and t is the time taken. Velocity is usually measured in meters per second or kilometers per hour.

Can Bird Watcher's Displacement and Velocity be negative?

Yes, both Displacement and Velocity can be negative. Negative Displacement indicates that the bird has moved in the opposite direction of the starting point, while negative Velocity indicates that the bird is moving in the opposite direction of the displacement. This is commonly seen when the bird changes direction during its flight.

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