Doubt about the 2nd position vector direction in a particle's movement

• mcastillo356
In summary, @Lnewqban failed a math test in July because he didn't study hard enough. He plans to try harder this semester and wants to ask for help.
mcastillo356
Gold Member
Homework Statement
We drive west at 75 km/h for 20 minutes and then follow a road that is oriented 40º to the south with respect to the original direction, driving at 90 km/h for some other 40 minutes. Calculate:
a) Total displacement
b) Celerity and velocity (vectorial) for all the travel
c) Draw a diagram of all the travel, including the length of each part of the displacement
Relevant Equations
Basic kinematics
I have not tried to make any calculation. It's nonsense, because I don't understand the statement. The first vector points to the west. Given a two dimensional coordinate system, the first vector is pointing to the left. I imagine geographical coordinates, north (+y), south (-y), west (-x), and east (+x). I think the first movement, in this coordinate system, is west (-x). But the second vector I think it can be drawn two ways; I mean that I can draw the second vector two valid ways, both starting at the end of the first vector: one, forward to the left, and down 40 degrees respect to the -x axis; and the second valid choice is to draw it backwards, I mean 40º respect the -x axis, but to the right. In this last choice, the car is also moving south, but turns back.
In both cases, the second vector moves 40 degrees downwards; but I think there are two possible choices respect the y axis: one pointing back to it; and the second (and also valid) following to the west.
Thanks!

When I read it, I envision the second vector going towards the left.

I understand your point and thought the same thing when reading through the problem statement. However, given that it just says "40º to the south with respect to the original direction", it suggests to me that it continues to the left.

mcastillo356 and Lnewqban
Master1022 said:
When I read it, I envision the second vector going towards the left.
...

“... a road that is oriented 40º to the south with respect to the original direction.”

mcastillo356 and etotheipi
@Lnewqban is right, there is no ambiguity here. A direction is represented by a vector (usually a unit vector), so you can translate 'original direction' to 'a unit vector pointing West'. There is then only one option!

Last edited by a moderator:
mcastillo356 and Lnewqban
Perfect! No doubt. The second vector must point west.
I am taking particular classes, to ensure a better result in september. In july I failed (3.3 over 10). I will need all the help available. They only give 1 hour, not a second more, to make the exam.
Good information that you've given.
Thanks!

Master1022, Lnewqban and etotheipi

1. What is the 2nd position vector in a particle's movement?

The 2nd position vector in a particle's movement refers to the displacement of the particle from its initial position to its second position. It is represented by a vector with magnitude and direction.

2. How is the direction of the 2nd position vector determined?

The direction of the 2nd position vector is determined by the line connecting the particle's initial position to its second position. This line is also known as the displacement vector.

3. Can the direction of the 2nd position vector change during the particle's movement?

Yes, the direction of the 2nd position vector can change during the particle's movement. This is because the particle's displacement can change as it moves, resulting in a change in the direction of the 2nd position vector.

4. How is the magnitude of the 2nd position vector calculated?

The magnitude of the 2nd position vector is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the horizontal and vertical components of the vector.

5. Is the 2nd position vector always in the same direction as the particle's velocity?

No, the 2nd position vector is not always in the same direction as the particle's velocity. The direction of the 2nd position vector is determined by the displacement of the particle, while the direction of the velocity vector is determined by the particle's motion. These two vectors may have different directions depending on the particle's movement.

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