Galilean form of the law of transformation of velocities

[user5]

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

 

[Doc Al]

May you help me with finding the angle, and what is "line of sight"?

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.

 

[user5]

I get -39°...not 15°...

 

[Doc Al]

I get -39°...not 15°...

Show how you got that.

 

[user5]

α=arctan(-62/76)

 

[Doc Al]

α=arctan(-62/76)

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]

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...

 

[Doc Al]

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...

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]

Are signs meaningless?

 

[Doc Al]

Are signs meaningless?

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]

I have drawn the angles but how are they related

 

[Doc Al]

I have drawn the angles but how are they related

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.

 

[user5]

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

 

[Doc Al]

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

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.

 

[user5]

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

 

[Doc Al]

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

(1) We are just comparing directions; dimensions are irrelevant.
(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.

 

[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!

 

[Doc Al]

Do I need to rotate the triangle of velocity?

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

The angle in this case -15°, is that right?

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

I'm grateful to you for your help!

You are most welcome.

 

[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?

 

[Doc Al]

Sorry for asking again...Do mean that velocity vector of 76 points toward the police while motorist have a velocity vector towards him of 62?

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]

Are the diagrams placed correctly, and then make use of alternating angles?

 

[Doc Al]

Are the diagrams placed correctly, and then make use of alternating angles?

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.

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.