Solving Vector Equations w/ A+B+C = 0

[nokitman]

Homework Statement

Vector A points in the negative x direction. Vector B points at an angle of 30 degrees above the positive x axis. Vector C has a magnitude of 15.0 m and points in a direction 40 degrees below the positive x axis. Given that vectors A + B + C = 0, find the magnitude of vector A and vector B

Homework Equations

Sin = opp/hyp

The Attempt at a Solution

For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Other than that I have no idea where to begin.

thanks,

 

[rock.freak667]

The Attempt at a Solution

For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Good. So we know C=11.49i-9.647j

so let's put A=ai+bj. It says A points in the negative x direction, so what should A really be ? (i.e. should the 'a' be +a or -a and what should 'b' equal to?)

So B acts at an angle of 30 degrees to the x-axis. If the magnitude of B is |B| then B=|B|(ci+dj)

so find A+B+C, grouping together the i and j terms.

 

[nokitman]

like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right?

 

[rock.freak667]

like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right?

Sorry I made a mistake, let's take out the |B| and just have B=ci+dj

You should get A+B+C = (11.49+a+c)i + (-9.647-b+d)j

once again now, if A=ai+bj is in the negative x direction, what is b equal to? And what sign should the a really have ?

 

[nokitman]

the "a" should be negative so A=-ai+bj, should the b also be negative?

 

[rock.freak667]

the "a" should be negative so A=-ai+bj, should the b also be negative?

right the 'a' should really be '-a'. So if the j component is the vertical component, and you know A is purely horizontal, what value should 'b' equal to?

 

[nokitman]

b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you

 

[rock.freak667]

b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you

yes this correct. So if it is equal to zero, that means both the i and j components are zero, so what is d?

 

[nokitman]

d= oi + oj

how does it get me to find the magnitude of A and B vectors?

 

[rock.freak667]

d= oi + oj

how does it get me to find the magnitude of A and B vectors?

no no

we have A+B+C = = (11.49 -a + c)i + (-9.647 + d)j = 0 =0i+0j.

so when you equate components, what is d equal to?

 

[nokitman]

d is zero?

 

[rock.freak667]

d is zero?

no if (-9.647 + d) =0 what is d? Do you know why (-9.647 + d) equal 0?

 

[nokitman]

sorry d is 9.647

 

[rock.freak667]

sorry d is 9.647

ok good. Now we know for a vector say R of magnitude |R|, acting at an angle θ to the x-axis can be represented as R= |R|cosθi+|R|sinθj


Can you now make a similar comparison to the vector B with magnitude |B|? Are you able to see how 'd' relates to |B| at the given angle?

 

[nokitman]

vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?

 

[rock.freak667]

vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?

yes, so now if d=|B|sin30 -> 9.647=|B|sinn30 what is |B| equal to?

When you get |B|, can you find what 'c' is equal to ?

 

[nokitman]

|B| = 11.139i + 19.294j?