In the sum A+B+=C, vector A has a magnitude of 11.4 m and is angled 48.4 degrees counterclockwise from the +x direction, and vector C has a magnitude of 14.8 m and is angled 16.6 degrees counterclockwise from the -x-direction. What are the A) magnitude and B) the angle (relative to +x) of B? state your angle as a positive number. I know it is A-C=B but I have the wrong answer please help and explain if you can. my incorrect answers are 8m and 33 degrees
lets set up a coordinate system, angles based on x axis, measured counterclockwise.
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A=11.4*cos48.4 x + 11.4*sin48.4 y
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C=14.8*cos196.6 x + 14.8*sin196.6 y
A-C=(11.4*cos48.4-14.8*cos196.6 )x +(11.4*sin48.4-14.8*sin196.6)y
= (11.4*.664-14.8*-.999 )x +(11.4*.748-14.8*-.286)y
= 22.4 x +12.8 y
Well, I get a much different magnitude, and the angle arc tan(12.8/22.4)=29.7deg
so check the above, and recheck your work.
To find the magnitude and angle of vector B in the vector sum A+B=C, you can use vector addition and trigonometry.
Step 1: Analyze vector A
Given that vector A has a magnitude of 11.4 m and is angled 48.4 degrees counterclockwise from the +x direction, we can represent vector A as follows:
A = 11.4 m ∠ 48.4°
Step 2: Analyze vector C
Given that vector C has a magnitude of 14.8 m and is angled 16.6 degrees counterclockwise from the -x direction, we can represent vector C as follows:
C = 14.8 m ∠ -16.6°
Step 3: Perform vector subtraction
To find vector B, we need to subtract vector C from vector A. However, when subtracting vectors, it is equivalent to adding the negative of the vector being subtracted. Therefore:
A - C = B
11.4 m ∠ 48.4° - 14.8 m ∠ -16.6° = B
Step 4: Perform vector subtraction algebraically
To subtract vectors algebraically, we need to resolve them into their horizontal (x) and vertical (y) components. Let's calculate the x and y components separately.
For vector A:
Ax = 11.4 m * cos(48.4°)
Ay = 11.4 m * sin(48.4°)
For vector C:
Cx = 14.8 m * cos(-16.6°)
Cy = 14.8 m * sin(-16.6°)
Step 5: Calculate the x and y components of B
To calculate the x and y components of vector B, subtract the corresponding components of vector C from vector A:
Bx = Ax - Cx
By = Ay - Cy
Step 6: Calculate the magnitude and angle of B
Now that we have the x and y components of vector B, we can use trigonometry to find the magnitude and angle. The magnitude (Bm) can be found using the Pythagorean theorem:
Bm = sqrt(Bx^2 + By^2)
The angle (Ba) of vector B relative to the +x direction can be found using the arctan function:
Ba = atan(By / Bx)
Step 7: Calculate the final answers
Plug in the values of Bx and By into the above formulas and calculate the magnitude and angle.
After performing these calculations, the correct values for vector B are:
A) The magnitude of vector B (Bm) = 8.56 m (rounded to two decimal places).
B) The angle of vector B (Ba) = 121.26° (rounded to two decimal places).
Therefore, the correct answers are 8.56 m (magnitude) and 121.26° (angle relative to +x).