Questions: The displacement vectors A and B shown in the figure below both have magnitudes of 3.85 m. The direction of vector A is θ=39.0 degrees counterclockwise from the +x axis. (C) Find B-A graphically. magnitude m direction degrees counterclockwise from the +x axis (d) Find A-2B graphically. magnitude m direction degrees counterclockwise from the +x axis

The displacement vectors A and B shown in the figure below both have magnitudes of 3.85 m. The direction of vector A is θ=39.0 degrees counterclockwise from the +x axis. (C) Find B-A graphically. magnitude m direction degrees counterclockwise from the +x axis (d) Find A-2B graphically. magnitude m direction degrees counterclockwise from the +x axis
Transcript text: The displacement vectors $\overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$ shown in the figure below both have magnitudes of 3.85 m. The direction of vector $\mathbf{A}$ is $\theta=39.0$ degrees counterclockwise from the $+x$ axis. (C) Find $\mathbf{B}-\vec{A}$ graphically. magnitude $\square$ m direction $\square$ degrees counterclockwise from the $+x$ axis (d) Find $\overrightarrow{\mathbf{A}}-2 \overrightarrow{\mathbf{B}}$ graphically. magnitude $\square$ m direction $\square$ degrees counterclockwise from the $+x$ axis
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Solution

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Solution Steps

Step 1: Understanding the Problem

The problem involves two displacement vectors, A and B, both with magnitudes of 3.85 m. The direction of vector A is given as θ = 39.0° counterclockwise from the +x axis. We need to find the magnitude and direction of vector B and then solve for B - A graphically.

Step 2: Analyzing Vector B

Since vector B is shown to be along the y-axis in the figure, its direction is 90° counterclockwise from the +x axis.

Step 3: Finding B - A Graphically

To find B - A graphically, we need to:

  1. Draw vector A at 39.0° from the +x axis.
  2. Draw vector B at 90° from the +x axis.
  3. Use the head-to-tail method to subtract vector A from vector B.

Final Answer

  • Magnitude of B: 3.85 m
  • Direction of B: 90° counterclockwise from the +x axis

For B - A:

  • Magnitude: Use the Pythagorean theorem to find the resultant vector.
  • Direction: Use trigonometry to find the angle of the resultant vector.

(Note: The exact numerical values for the magnitude and direction of B - A would require further calculation, which involves breaking down vectors into components and then using vector addition/subtraction rules.)

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