Solving for Vector Expression: 12.0 m and 170° (i+j)

[chocolatelover]

Homework Statement

Find an expression in component form for 12.0 m and 170° (i+j)

Homework Equations

Ax=Acostheta
Ay=Asintheta

The Attempt at a Solution

I was thinking about using one of these equations, but I don't know which one to use or if there is another way of doing it. Does it matter which one I use?

Would it be

12.0cos170? but I don't know where the i or the j would go

Could someone please show me how to set this problem up?

Thank you very much

 

[ranger]

Yes, it matters which one you use for a particular component. Why not draw the vector on a graph? To break it up into its components: the x component (i) is the first equation you've written down, the y (j) component is the second one. You can prove this to yourself by using the graph and some trigonometry.

As an additional check, you can go back from i and j to polar notion. The magnitude is essentially what I told you in the other thread i.e. |A|. The angle is tan^-1 (y/x) (thats the inverse tangent)

EDIT: An important note about evaluating tan^-1() using a calculator. If your components are in quadrants one and four, your answer in degrees is correct. However if your components are in the second and third quadrants, your answer is off by 180 degrees. Therefore you have to add or subtract 180 degrees from the answer tan^-1() gives you. It does not matter if you add or subtract, as they are both correct. Your problem is a classic example of this. Try it!

 

[mjsd]

i is usually the x direction
j is usually the y direction
draw a diagram, and see the projection onto the x and y axes to visualise, then use trig to determine which equation to use.

 

[chocolatelover]

Thank you very much

Does 12sin10 look right for the i (x component)?

Thank you

 

[chocolatelover]

Can someone please tell me if this is correct?

Thank you

 

[mjsd]

Thank you very much

Does 12sin10 look right for the i (x component)?

Thank you

one thing is unclear here... is the angle measuring from the positive x-axis?
draw a diagram if unsure what is what.

 

[chocolatelover]

Thank you

is the angle measuring from the positive x-axis?

Yes. Would i be 12cos10 and would j be 12sin10? Would I use 10°? (180-170)

Thank you

 

[chocokat]

Yes. Would i be 12cos10 and would j be 12sin10? Would I use 10°? (180-170)

Yes, just be careful. 170° is in the 2nd quadrant, so your 'x' or 'i' value will be negative. So, it's actually -(12cos10).

 

[chocolatelover]

Thank you very much

Regards