In the sum A+ B =C , vecto rA has a magnitude of 11.0 m and is angled 32.0° counterclockwise from the +x direction, and vector C has a magnitude of 15.0 m and is angled 18.0° counterclockwise from the -x direction. What are the magnitude and the angle (relative to +x) of B?
B = C - A in vector notation. Subtracting a vector is the same as adding its negative. Do the vector subtraction for the answer. Using the components method will get you the x and y components of B. From those two components, get the magnitude and direction
To find the magnitude and angle of vector B in the equation A + B = C, we'll need to use vector addition and trigonometry.
First, let's break down vector A and vector C into their components.
For vector A:
- The magnitude of vector A is 11.0 m.
- The angle of vector A is 32.0° counterclockwise from the +x direction.
To find the x-component (Ax) and y-component (Ay) of vector A, we use trigonometry:
Ax = A * cos(theta_A)
Ay = A * sin(theta_A)
Substituting the given values:
Ax = 11.0 m * cos(32.0°)
Ay = 11.0 m * sin(32.0°)
Next, let's calculate vector C:
- The magnitude of vector C is 15.0 m.
- The angle of vector C is 18.0° counterclockwise from the -x direction.
Again, using trigonometry, we can find the x-component (Cx) and y-component (Cy) of vector C:
Cx = C * cos(theta_C)
Cy = C * sin(theta_C)
Plugging in the values:
Cx = 15.0 m * cos(18.0°)
Cy = 15.0 m * sin(18.0°)
Now, let's find the components of vector B.
Since A + B = C, we can write the equation in terms of components:
(Ax + Bx) i + (Ay + By) j = Cx i + Cy j
Comparing the coefficients of i and j on both sides, we get:
Ax + Bx = Cx
Ay + By = Cy
Rearranging the equations, we can solve for Bx and By:
Bx = Cx - Ax
By = Cy - Ay
Substituting the component values we calculated earlier, we can find Bx and By.
Finally, to find the magnitude and angle of vector B, we use the components Bx and By:
Magnitude of B = sqrt(Bx^2 + By^2)
Angle of B = atan(By/Bx)
Applying these calculations, we can find the magnitude and angle of vector B in the given equation.