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

[mcastillo356]

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!

 

[Master1022]

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.

 

[Lnewqban]

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.”

 

[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!

 

[mcastillo356]

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!