How Can I Learn Vector Basics for Physics Homework?

[chewykid92]

Need help on my physics homework -- vectors

Hey, this is my first time using this website, but my friend told me it was really helpful when he was in college taking physics, so here it goes.

I need help on my physics hw, I have never taken physics before. So i uploaded a picture of my hw, DON'T GIVE ME THE ANSWER, just simply guide me through the process of it because I want to learn how to do it.

 

[CAF123]

Set up a coordinate system: $\vec{D} = 2\,cm\hat{x}$ means there is a displacement of 2cm along the x-axis taking (0,0) as the initial starting point. If instead, the displacement is 5 times as much, then you have gone along the x-axis 5 times as much relative to the origin. So therefore, what is the $a$ in $\vec{D'} = a\vec{D}?$

For the second part, the words mean in the coordinate system defined above, vector S is at angle of 30^o with respect to the positive x axis. Do you know how to write this vector in component form?

 

[chewykid92]

no, i don't know how to write it in vector component form.

 

[CAF123]

Think of a right angled triangle. You should know from elementary trigonometry that $\sinθ = \frac{opp}{hyp}$ and $\cosθ = \frac{adj}{hyp}.$ The hypoteneuse here can be thought of as the actual vector and the other two sides its components. If you label the 'opposite' side of the traingle, $S_y$ and the 'adjacent' side $S_x$ and the hypotenuse $S$, you should be able to get that $Ssinθ = S_y$ and $Scosθ = S_x.$ These are the components of the vector S.

Do you see this?
In terms of vector notation, we write $\vec{S} = Scosθ\hat{x} + Ssinθ\hat{y}.$

Ok, now what is $-\vec{S}?$

 

[chewykid92]

Thanks for the reply, but unfortunately, I did not see what you posted quick enough, turned in my homework already, but when I got back and saw this reply, this was really helpful, so maybe next time if there is another problem like this, I can compare what to do, thank you for your help!

 

[berkeman]

Thanks for the reply, but unfortunately, I did not see what you posted quick enough, turned in my homework already, but when I got back and saw this reply, this was really helpful, so maybe next time if there is another problem like this, I can compare what to do, thank you for your help!

The next time you post here in Homework Help, be sure to use the HH Template that you are provided. Fill out the sections for the Relevant Equations and show your Attempt at a Solution. That is part of the rules here at the PF, and is meant to help you learn how to learn.