Write the steps and the entire example in your Engineering Notebook. You will use this as a reference for future problems of this type.
Follow these steps to find the resultant vector. note: there are other trigonometric laws such as law of sines and law of cosines that could be used to do the same process. The method I chose will allow you to use the trigonometry that you already know and lead us into solving truss problems.
Step 1. Identify the sense of each vector
Step 2. Draw a Free Body Diagram of each vector
Step 3. Find the x and y component of each vector
Step 4. Find the sum of each component
Step 5. Draw a resultant Free Body Diagram from the component sums
Step 6. Use Pythagorean Theorem to find the resultant.
Step 7. Use an inverse Trigonometry ratio to find the resultant angle.
Step 8. Make sure your answer makes sense.
example:
Vector A has a magnitude of 10 at an angle of zero degrees. Vector B has magnitude of 5 with an angle of 50 degrees. Find the resultant magnitude and angle.
What is the sense of vector A? What is the sense of vector B?
Draw an FBD for each vector including the angle and components.
Use the sin and cos to find the x and y components of each vector.
Add the x components together. Add the y components together.
Draw an FBD with these component sums.
Use Pythagorean Theorem to find the resultant.
Use an inverse trigonometric ratio to find the resultant angle.