- #1
Galilean form of the law of transformation of velocities
- Thread starter user5
- Start date
-
- Tags
- Form Galilean Law Transformation
Click For Summary
Homework Help Overview
The discussion revolves around finding an angle related to the velocities of a police car and a motorist, specifically in the context of the Galilean transformation of velocities. Participants are exploring the concept of "line of sight" and its implications for determining the angle between the two vehicles' velocities.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- Participants are attempting to calculate the angle based on the velocities of the police car and motorist, with some confusion about the definition of "line of sight." There are discussions about the signs of angles and how to represent the vectors graphically. Questions arise regarding the relationships between the angles and the necessity of drawing accurate diagrams.
Discussion Status
The discussion is active, with various participants sharing their calculations and questioning the meanings of their results. Some guidance has been offered regarding the drawing of diagrams and the interpretation of angles, but there is no explicit consensus on the correct approach or final answer yet.
Contextual Notes
Participants are navigating through potential misunderstandings about vector directions and the relevance of angle signs. There is an emphasis on visual representation and the geometric relationships between the vectors involved.
- #2
Doc Al
Mentor
- 45,584
- 2,459
By "line of sight" they mean the direction in which the police car is moving. (Where they would be looking straight ahead.) So imagine an axis extending forward from the police car.user5 said:
To find the angle, figure out the velocity of the motorist in the frame of the police car.
- #3
user5
- 38
- 0
I get -39°...not 15°...
Last edited:
- #4
Doc Al
Mentor
- 45,584
- 2,459
Show how you got that.user5 said:
- #5
user5
- 38
- 0
α=arctan(-62/76)
- #6
Doc Al
Mentor
- 45,584
- 2,459
Ah, I was wrong about what they meant by "line of sight". Line of sight is the line directed from the police car to the motorist. Find the angle with respect to that line and you'll get the answer given.user5 said:
- #7
user5
- 38
- 0
I'm confused, now I got -54° and what does the minus sign mean in that situation, may you give some more details about the solution...
- #8
Doc Al
Mentor
- 45,584
- 2,459
Don't worry about signs. Instead, draw yourself a picture. Show the line of sight (which is based on distances) and then add the direction of the velocity, which you already found. Find the angle between those two.user5 said:
- #9
user5
- 38
- 0
Are signs meaningless?
- #10
Doc Al
Mentor
- 45,584
- 2,459
No, but rather than rely on the mechanical use of a formula you would be better off simply drawing the relevant angles. Then you wouldn't have questions about signs.user5 said:
- #11
- #12
Doc Al
Mentor
- 45,584
- 2,459
The first diagram is drawn correctly: The hypotenuse represents the line of sight.user5 said:
The second diagram needs to be redrawn to represent the sum of those velocity vectors. That vector will represent the relative velocity.
- #13
user5
- 38
- 0
76 need to be reversed ...How do those drawings show me that I need to subtract those angles?
Last edited:
- #14
Doc Al
Mentor
- 45,584
- 2,459
When adding vectors graphically you must have the tail of one start at the head of the other.user5 said:
You want the angle that the velocity makes with the line of sight. Draw them both on the same diagram and find the angle between them.
- #15
- #16
Doc Al
Mentor
- 45,584
- 2,459
(1) We are just comparing directions; dimensions are irrelevant.user5 said:
(2) Your diagram is still not right. You want: tail - head - tail - head. You have: head - tail - tail - head.
(3) Find the angle each direction vector makes with the horizontal; then you can find the angle they make with each other by subtracting.
- #17
- #18
Doc Al
Mentor
- 45,584
- 2,459
It's not a question of rotating the triangle, but drawing it correctly. Note that the velocity vector will point towards the police car.user5 said:
Yes, but don't worry about the minus sign. I'm sure they just want the magnitude.
You are most welcome.
- #19
user5
- 38
- 0
Sorry for asking again...Do you mean that velocity vector of 76 points toward the police while motorist have a velocity vector towards him of 62?
Last edited:
- #20
Doc Al
Mentor
- 45,584
- 2,459
The velocity vector of the motorist with respect to the Police will point somewhat towards the Police. Not exactly of course--it will make an angle of 15° to the line of sight. In your diagram in post #17 the red arrow, which I presume represents the velocity of the motorist with respect to the police, points in the wrong direction.user5 said:
- #21
- #22
Doc Al
Mentor
- 45,584
- 2,459
It's hard to say from your diagram, but I think you have the correct angles for the line of sight and for the velocity.user5 said:
To see what's going on, do this. On the original diagram, the one that described the problem, draw a line from motorist to police. That's the line of sight. You already figured out the angle it makes with the horizontal.
Then, on that same diagram, draw the velocity vector (the velocity of the motorist relative to the police) emanating from the position of the motorist. You have already figured out the angle that that vector makes with the horizontal.
Then you'll be able to figure out the angle between those two lines, using a bit of geometry.