Splitting a vector into two

[koat]

hello everybody
can somebody help me how to do this exercise. i don't know how to start...
exercise:
a van is traveling 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 can't use pythagoras as there's no right angle.

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

 

[radou]

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 don't understand it.
whats a cartesian?
in class we used to draw the vertical and horizontal component for such exercises.
but i don't 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 don't understand it.
whats a cartesian?
in class we used to draw the vertical and horizontal component for such exercises.
but i don't 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.