# Splitting a vector into two

koat
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

Homework Helper
What does change mean? Surely not addition.

40 degrees east of north means that you "rotate" your direction for 40 degrees east of north. :)

noon0788
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).

koat
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

koat
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:

PhaseShifter
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?

koat
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?

PhaseShifter
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: