Using a Protractor: In order to accurately measure the angle, we first need to understand how to use a protractor correctly. Follow these steps to ensure the correct measurements:
1. Draw a 4.0 cm long vector, A, on the dashed line from the origin to the upper right.
2. Align the bottom of the protractor parallel with the X-axis.
3. Move the protractor so the origin of the protractor is superimposed on the origin of the coordinate system.
4. With 0° pointing towards the +X-axis, read the angle that the vector makes relative to the +X-axis. In some cases, it may be helpful to extend the vector with a dashed line to ensure a more reliable measurement.
5. Now measure the angle of vector A relative to +X. OA°.
6. Draw the components of this vector on your X- and Y-coordinate axes and label them as Ax and Ay.
7. Use the ruler to find the values of these components: Ax, Ay (Make sure to include units).
8. Using the measured angle, OR calculate the x and y components using the formulas:
Ax = |A| cos(θ)
Ay = |A| sin(θ)
(Make sure to include units).
9. Do these agree with your measured values? If not, double-check your angle measurement.
10. Now, draw a 3 cm long vector, B, from the origin to the upper left along the dashed line.
11. Repeating the steps listed above, determine OB°.
12. Calculate Bx and By (Measured).
13. Calculate Bx and By (Calculated).
14. Finally, calculate the resultant vector, R:
Rx
Ry
R
θr