Galilean form of the law of transformation of velocities

1. Aug 8, 2013

user5

May you help me with finding the angle, and what is "line of sight"?(the final answer is 15°)

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2. Aug 8, 2013

Staff: Mentor

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.

To find the angle, figure out the velocity of the motorist in the frame of the police car.

3. Aug 8, 2013

user5

I get -39°...not 15°...

Last edited: Aug 8, 2013
4. Aug 8, 2013

Staff: Mentor

Show how you got that.

5. Aug 8, 2013

user5

α=arctan(-62/76)

6. Aug 8, 2013

Staff: Mentor

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.

7. Aug 8, 2013

user5

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. Aug 8, 2013

Staff: Mentor

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.

9. Aug 8, 2013

user5

Are signs meaningless?

10. Aug 8, 2013

Staff: Mentor

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.

11. Aug 8, 2013

user5

I have drawn the angles but how are they related

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12. Aug 8, 2013

Staff: Mentor

The first diagram is drawn correctly: The hypotenuse represents the line of sight.

The second diagram needs to be redrawn to represent the sum of those velocity vectors. That vector will represent the relative velocity.

13. Aug 8, 2013

user5

76 need to be reversed ...How do those drawings show me that I need to subtract those angles?

Last edited: Aug 8, 2013
14. Aug 8, 2013

Staff: Mentor

When adding vectors graphically you must have the tail of one start at the head of the other.

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. Aug 8, 2013

user5

But they have different dimensions...and why to subtract?

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16. Aug 8, 2013

Staff: Mentor

(1) We are just comparing directions; dimensions are irrelevant.
(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. Aug 8, 2013

user5

Do I need to rotate the triangle of velocity? The angle in this case -15°, is that right?
I'm grateful to you for your help!

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18. Aug 8, 2013

Staff: Mentor

It's not a question of rotating the triangle, but drawing it correctly. Note that the velocity vector will point towards the police car.

Yes, but don't worry about the minus sign. I'm sure they just want the magnitude.

You are most welcome.

19. Aug 8, 2013

user5

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: Aug 8, 2013
20. Aug 8, 2013

Staff: Mentor

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.