Determining Displacement Using Vector Components

In summary, the conversation is about a physics problem involving a light plane that traveled from Shelburne, NS to Moncton, NB with a stop in Saint John, NB. The problem is to calculate the average velocity of the plane for the entire trip. The conversation includes calculations and discussions about the given information, including compass directions and distances. The final conclusion is that the given answer in the book may be incorrect and the individual should submit their answer instead. The conversation also briefly touches on the interpretation of a heading, which is 84 degrees North of West in this case.
  • #1
killaI9BI
51
0

Homework Statement



This problem has had me puzzled for hours. I really appreciate any help you can provide.

A light plane leaves Shelburne, NS and flies 195km [N15°W] to Saint John, NB. After picking up a passenger, it flies to Moncton, NB which is 149km [N33°E]. The entire trip took 3.75h.

Calculate the average velocity of the plane for the entire trip from Shelburne, NS to Moncton, NB.

Homework Equations



a2 + b2 = c2
tan Θ = y-coordinates/x-coordinates

The Attempt at a Solution



dsjx = (-195) X cos75 = (-50.47)km W
dsjy = 195 X sin75 = 188.36km N
dmx = 149 X cos57 = 81.15km E
dmy = 149 X sin57 = 124.96km N
dx = (-50.47) + 81.15 = 30.68km E
dy = 188.36 + 124.96 = 313.32km N

r2 = 30.682 + 313.322
r2 = 99110.68
r = 314.8
314.8/3.75 = 83.95/h

tan θ = 313.32/30.68 = 10.21
θ = 84.4

The average velocity is 84km/h W 84 N.

The books answer is 48km/h [W29°N]

 
Physics news on Phys.org
  • #2
I agree with your answer. I'd guess one of the given pieces of information has a wrongly stated compass direction, but I haven't been able to figure out exactly what. If these are real places, consult a map.
 
  • #3
Thank you. I did consult a map which says the distance between Shelburne NS and Moncton, NB is 262km which appears to be different than both mine and the books answers. I've double and triple checked the information provided and it's all accurate.

I'm doing grade 11 physics via correspondence with nobody to ask questions to. Questions like these sort of ruin my flow. Do you think I should submit this answer?
 
  • #4
How do you interpret the heading W 84 N?
 
  • #5
killaI9BI said:
Thank you. I did consult a map which says the distance between Shelburne NS and Moncton, NB is 262km which appears to be different than both mine and the books answers. I've double and triple checked the information provided and it's all accurate.
OK. The 33 degrees stated looks a bit low to me. Judging from Google maps it's more like 40 degrees, but that could be deceptive. Anyway, your answer is a lot closer to reality than the book answer. Submit it.
 
  • Like
Likes 1 person
  • #6
olivermsun said:
How do you interpret the heading W 84 N?


Sorry for the delayed response

84 degrees North of West
 

Related to Determining Displacement Using Vector Components

1. What is displacement?

Displacement is a vector quantity that measures the change in position or location of an object in a specified direction. It is typically represented by an arrow pointing from the initial position to the final position of the object.

2. How is displacement calculated using vector components?

To calculate displacement using vector components, you must first determine the x and y components of the displacement vector. This can be done using trigonometric functions and the magnitude and direction of the displacement vector. Once the components are determined, they can be added together using vector addition to find the overall displacement.

3. What is the difference between displacement and distance?

Displacement is a vector quantity that measures the change in position and includes both magnitude and direction. Distance, on the other hand, is a scalar quantity that measures the total amount of ground covered, regardless of direction. Displacement takes into account both the starting and ending points, while distance does not.

4. Can displacement be negative?

Yes, displacement can be negative. This occurs when an object moves in the opposite direction of its initial position. In such cases, the displacement vector will have a negative magnitude, indicating a change in position in the opposite direction.

5. How is displacement represented graphically?

Displacement can be represented graphically using a coordinate system, such as a Cartesian plane. The initial position of the object is represented by the origin (0,0), and the final position is represented by a point with coordinates (x,y). The displacement vector is then drawn from the origin to the final point, indicating the direction and magnitude of the displacement.

Similar threads

Calculate electric force using Coulomb's law (vector components are the struggle)
    • Introductory Physics Homework Help
Replies
3
Views
165

Hot Threads

Recent Insights

Back
Top