Vectors in two dimensional motion: Need help with starting

[mrrocketknigh]

Homework Statement

A car travels 20.0 km due north and then 35.0 km in a direction of 60(degrees) west of north. Using a graph (that you must construct yourself as the book says... sorry for the inconvenience :/) and find the magnitude and direction of a single vector that gives the net effect of the car's trip. This vector is called the car's RESULTANT DISPLACEMENT.

Homework Equations

You must know the properties of vectors, but even with that knowledge, I can't seem to find the answer. The ANSWER SHOULD BE 48 km. Can someone explain to me why?

The Attempt at a Solution

I added vector A with vector B and got about 55 km. Why am I wrong? Am I missing something?

 

[cepheid]

In general, vectors don't add like that. You can't add up the magnitudes of the two vectors directly, because they aren't in the same direction. The resultant vector should be a vector that indicates how far away the car ended up from its starting point. Try looking at this:

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec7

 

[mrrocketknigh]

In general, vectors don't add like that. You can't add up the magnitudes of the two vectors directly, because they aren't in the same direction. The resultant vector should be a vector that indicates how far away the car ended up from its starting point. Try looking at this:

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec7

Alright, thanks for the link. But, I still don't know if this is correct, but I managed to get this. I added both vectors, giving me approx. 55 ft. Then I took the square root of that to get approx. 7 ft. I then subtracted 7 from 55 to get the answer: 48 ft. Is that the basic way of doing these problems?

 

[cepheid]

Alright, thanks for the link. But, I still don't know if this is correct, but I managed to get this. I added both vectors, giving me approx. 55 ft.

Huh? How did you do that? I just finished telling you that you cannot add up the magnitudes of the vectors directly. This should be clear from the diagram. When you add vector A to vector B (which you do by placing them "tip" to "end"), you can clearly see that the length of the resultant R is not equal to the sum of the lengths of A and B. The three form a triangle, and to get the side length of R, you either need to (1) use geometry (based on what you know about that triangle and the lengths of sides A and B), OR (2) you need to resolve A and B into horizontal and vertical components, and add those up separately to get the horizontal component of R and the vertical component of R. Then you can use those to get the magnitude of R.

Either method (1) or (2) will work.

Then I took the square root of that to get approx. 7 ft. I then subtracted 7 from 55 to get the answer: 48 ft. Is that the basic way of doing these problems?

Okay this doesn't make any sense whatsoever. The square root of 55 is NOT 7, and you haven't given any indication as to why you tried these steps. Don't just try random things. Examine the diagram and try to understand how to solve for the length of the third side of the triangle given that you know what the other two are.

 

[rwisz]

Hi there,

It seems like you are on the right track with using vector addition to find the resultant displacement of the car's trip. However, there are a few things to keep in mind when adding vectors in two dimensional motion.

First, make sure you are using the correct direction for each vector. In this case, the car travels 20.0 km due north and then 35.0 km in a direction of 60 degrees west of north. This means that vector A should be pointing directly upwards and vector B should be pointing in a direction 60 degrees to the left of upwards.

Next, remember that when adding vectors, you need to take into account both magnitude and direction. This means that you cannot simply add the magnitudes of vector A and vector B to get the resultant displacement. Instead, you need to use vector addition, which involves breaking each vector into its x and y components and then adding the components separately.

Using vector addition, you should get a resultant displacement of approximately 48 km, which is the correct answer. To understand why this is the correct answer, you can think of it as the car traveling 48 km in a direction that is a combination of the two original directions (due north and 60 degrees west of north).

I hope this helps and good luck with your homework!