Vector A has a magnitude of 9.00units and makes an angle of 49.0° counter-clockw

Question

Vector A has a magnitude of 9.00units and makes an angle of 49.0° counter-clockwisefrom the positive x-axis. Vector B has a magnitude of8.00 units and is directed along the negativex-axis. (a) Using graphical methods, find thevector sum A + B. Magnitude of A + B: 1 units Direction of A + B: 2° counterclockwise from+x-axis
(b) Using graphical methods, find the vector difference A -B. Magnitude of A - B: 3 units Direction of A - B: 4° counterclockwise from+x-axis (a) Using graphical methods, find thevector sum A + B. Magnitude of A + B: 1 units Direction of A + B: 2° counterclockwise from+x-axis
(b) Using graphical methods, find the vector difference A -B. Magnitude of A - B: 3 units Direction of A - B: 4° counterclockwise from+x-axis Magnitude of A + B: 1 units Direction of A + B: 2° counterclockwise from+x-axis

Explanation / Answer

Here is an example just likeit.       Vector A has a magnitude of 9.30 units andmakes an angle of 40.5° counter-clockwise from the positivex-axis. Vector B has a magnitude of 8.00 units and is directedalong the negative x-axis.

(a) Using graphical methods, find the vector sum A + B. Magnitudeof

A + B: ???? units

Direction of A + B: ???° counterclockwise from +x-axis

(b) Using graphical methods, find the vector difference A - B.

Magnitude of A - B: ???? units

Direction of A - B: ???° counterclockwise from +x-axis

• Ok, the problem want the "graphical" solution,but I will use the analytical solution, then show a hint how tosolve
  
  Va = 9.3 cos 45 i + 9.3 sin 45 j
  
  Vb = -- 8 i
  
  Part a
  
  Va + Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] + [ -- 8 i ] = -- 1.42 i+ 6.58 j
  
  The resultant will direct in the second quadrant,
  
  tan angle = -- 1.42 / 6.58
  
  >>> Angle = 167.8 degrees.
  
  Part b
  
  Va -- Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] -- [ -- 8 i ] = 14.6 i +6.58 j
  
  Tan angle = 14.6 / 6.58
  
  >> Angle = 65.7 degrees.
  
  ______________________________
  
  Graphical solution:
  
  Now you have a hint where the resultant vector will point, part a168 deg from x, and part b 65 degree.
  
  All you should do is :
  
  1- Draw the vecor A pointing 45 degrees to x axis, and it's lengthwith scale factor on your notebook.
  
  2- Do the same for B. But start drawing B from the "head" of thevecor A.
  
  3- Connect the head of vector B to tail of vector A .. this vectoris the resultant one.
  
  Do this for part a and part b .. each on a separate graph.

• Ok, the problem want the "graphical" solution,but I will use the analytical solution, then show a hint how tosolve
  
  Va = 9.3 cos 45 i + 9.3 sin 45 j
  
  Vb = -- 8 i
  
  Part a
  
  Va + Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] + [ -- 8 i ] = -- 1.42 i+ 6.58 j
  
  The resultant will direct in the second quadrant,
  
  tan angle = -- 1.42 / 6.58
  
  >>> Angle = 167.8 degrees.
  
  Part b
  
  Va -- Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] -- [ -- 8 i ] = 14.6 i +6.58 j
  
  Tan angle = 14.6 / 6.58
  
  >> Angle = 65.7 degrees.
  
  ______________________________
  
  Graphical solution:
  
  Now you have a hint where the resultant vector will point, part a168 deg from x, and part b 65 degree.
  
  All you should do is :
  
  1- Draw the vecor A pointing 45 degrees to x axis, and it's lengthwith scale factor on your notebook.
  
  2- Do the same for B. But start drawing B from the "head" of thevecor A.
  
  3- Connect the head of vector B to tail of vector A .. this vectoris the resultant one.
  
  Do this for part a and part b .. each on a separate graph.

Ok, the problem want the "graphical" solution,but I will use the analytical solution, then show a hint how tosolve

Va = 9.3 cos 45 i + 9.3 sin 45 j

Vb = -- 8 i

Part a

Va + Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] + [ -- 8 i ] = -- 1.42 i+ 6.58 j

The resultant will direct in the second quadrant,

tan angle = -- 1.42 / 6.58

>>> Angle = 167.8 degrees.

Part b

Va -- Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] -- [ -- 8 i ] = 14.6 i +6.58 j

Tan angle = 14.6 / 6.58

>> Angle = 65.7 degrees.

______________________________

Graphical solution:

Now you have a hint where the resultant vector will point, part a168 deg from x, and part b 65 degree.

All you should do is :

1- Draw the vecor A pointing 45 degrees to x axis, and it's lengthwith scale factor on your notebook.

2- Do the same for B. But start drawing B from the "head" of thevecor A.

3- Connect the head of vector B to tail of vector A .. this vectoris the resultant one.

Do this for part a and part b .. each on a separate graph. Ok, the problem want the "graphical" solution,but I will use the analytical solution, then show a hint how tosolve

Va = 9.3 cos 45 i + 9.3 sin 45 j

Vb = -- 8 i

Part a

Va + Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] + [ -- 8 i ] = -- 1.42 i+ 6.58 j

The resultant will direct in the second quadrant,

tan angle = -- 1.42 / 6.58

>>> Angle = 167.8 degrees.

Part b

Va -- Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] -- [ -- 8 i ] = 14.6 i +6.58 j

Tan angle = 14.6 / 6.58

>> Angle = 65.7 degrees.

______________________________

Graphical solution:

Now you have a hint where the resultant vector will point, part a168 deg from x, and part b 65 degree.

All you should do is :

1- Draw the vecor A pointing 45 degrees to x axis, and it's lengthwith scale factor on your notebook.

2- Do the same for B. But start drawing B from the "head" of thevecor A.

3- Connect the head of vector B to tail of vector A .. this vectoris the resultant one.

Do this for part a and part b .. each on a separate graph. Ok, the problem want the "graphical" solution,but I will use the analytical solution, then show a hint how tosolve

Va = 9.3 cos 45 i + 9.3 sin 45 j

Vb = -- 8 i

Part a

Va + Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] + [ -- 8 i ] = -- 1.42 i+ 6.58 j

The resultant will direct in the second quadrant,

tan angle = -- 1.42 / 6.58

>>> Angle = 167.8 degrees.

Part b

Va -- Vb = [ 9.3 cos 45 i + 9.3 sin 45 j ] -- [ -- 8 i ] = 14.6 i +6.58 j

Tan angle = 14.6 / 6.58

>> Angle = 65.7 degrees.

______________________________

Graphical solution:

Now you have a hint where the resultant vector will point, part a168 deg from x, and part b 65 degree.

All you should do is :

1- Draw the vecor A pointing 45 degrees to x axis, and it's lengthwith scale factor on your notebook.

2- Do the same for B. But start drawing B from the "head" of thevecor A.

3- Connect the head of vector B to tail of vector A .. this vectoris the resultant one.

Do this for part a and part b .. each on a separate graph.

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