• Support PF! Buy your school textbooks, materials and every day products Here!

Splitting a vector into two

  • Thread starter koat
  • Start date
  • #1
40
0
hello everybody
can somebody help me how to do this exercise. i dont know how to start....
exercise:
a van is travelling north at a speed of 28m/s.after turning a corner it is heading 40° east of north at 25 m/s.
work out the change in velocity of the van.

first of all what i don't understand is what exactly do they mean with east of north? do they mean northeast?
i tried to work out the resultant but thaats not possible as i cant use pythagoras as there's no right angle.

i would be really happy to get some help
thanks in advance :)
 

Answers and Replies

  • #2
radou
Homework Helper
3,115
6
What does change mean? Surely not addition.

40 degrees east of north means that you "rotate" your direction for 40 degrees east of north. :)
 
  • #3
22
0
Let's start off in polar coordinates assuming that north is in the direction of the positive y-axis and call the first velocity/angle V1 and the second V2.
(in polar coordinates, an ordered pair is (r,theta) where r is the magnitude and theta is the angle)

V1 = (28, 90)
V2 = (25, 50)

Now if you're looking for a simple change in velocity, it'd be 3m/s. But I'm guessing that'd be too easy. If you convert the polar coordinates to cartesian, then you can find the change in velocity with respect to y (north) and x (east).
 
  • #4
40
0
Let's start off in polar coordinates assuming that north is in the direction of the positive y-axis and call the first velocity/angle V1 and the second V2.
(in polar coordinates, an ordered pair is (r,theta) where r is the magnitude and theta is the angle)

V1 = (28, 90)
V2 = (25, 50)

Now if you're looking for a simple change in velocity, it'd be 3m/s. But I'm guessing that'd be too easy. If you convert the polar coordinates to cartesian, then you can find the change in velocity with respect to y (north) and x (east).
thanks for the explanation
but i still dont understand it.
whats a cartesian?
in class we used to draw the vertical and horizontal component for such exercises.
but i dont know how to apply it here
 
  • #5
40
0
What does change mean? Surely not addition.

40 degrees east of north means that you "rotate" your direction for 40 degrees east of north. :)
i thought the change is 3 but that is apparently wrong:uhh:
 
  • #6
277
1
thanks for the explanation
but i still dont understand it.
whats a cartesian?
in class we used to draw the vertical and horizontal component for such exercises.
but i dont know how to apply it here
Draw a map with north on the vertical axis.
The original velocity is 28 m/s in the vertical direction on the map.
The speed after the change is 25 m/s, but the direction has also shifted to the right, forming a 40 degree angle with the original vector at the origin.

What is the difference between those two vectors?
 
  • #7
40
0
Draw a map with north on the vertical axis.
The original velocity is 28 m/s in the vertical direction on the map.
The speed after the change is 25 m/s, but the direction has also shifted to the right, forming a 40 degree angle with the original vector at the origin.

What is the difference between those two vectors?
is that right?
28²+25² and then square root it?
 
  • #8
277
1
is that right?
28²+25² and then square root it?
Not at all.
1) The vectors form a 40 degree angle, not a 90 degree angle The Pythagorean theorem is useless here.
2) The change is the difference between the vectors, not the sum--so even if the angle had been 90 degrees the Pythagorean theorem would be useless.
3) The problem asks for change in velocity, not change in speed. The answer will be a vector, not a scalar.

You need to learn how to subtract vectors, and you need to learn how to find the vertical and horizontal components of a diagonal vector (this will involve some trigonometry).

Try drawing a diagram of the problem and see if that helps you understand better.
 
Last edited:

Related Threads on Splitting a vector into two

  • Last Post
Replies
1
Views
1K
Replies
14
Views
2K
Replies
5
Views
594
Replies
6
Views
2K
Replies
12
Views
679
  • Last Post
Replies
2
Views
489
  • Last Post
Replies
0
Views
3K
Replies
6
Views
863
Replies
7
Views
3K
Top