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Background: A single vector may be analyzed by resolving the vector into horizontal (x) and vertical (y) components. This information then allows calculation of the magnitude (via Pythagorean Theorem) and angle (via trigonometry) of the original vector. Two or more vectors can be added together graphically using the head-to-tail method or mathematically using component addition to determine a vector sum or resultant vector. This vector can then be resolved into components and analyzed. Procedure: For each problem, vectors A, B and C are shown. 1) Sketch the head-to-tail addition of A+B+C on the empty grid, labeling each vector. 2) Draw and label the resultant (R) on the grid. 3) Complete the table by recording the x and y components for vectors A, B, and C. Use a positive sign (+) to indicate East or North; use a negative (-) to indicate a West or South. 4) Sum the components to determine the components of the resultant. Record the magnitude and direction of each component of the resultant. Use a positive sign (+) to indicate East or North; use a negative (-) to Indicate a West or South. 5) Verify your work. The resultant drawn on the grid should have the same components as shown in the table. If not, carefully repeat steps 1-4 to find your error. 6) Use the Pythagorean theorem and SOH CAH TOA to determine the magnitude and direction of R. a+ b'= c

Background: A single vector may be analyzed by resolving the vector into horizontal (x) and vertical (y) components. This information then allows calculation of the magnitude (via Pythagorean Theorem) and angle (via trigonometry) of the original vector. Two or more vectors can be added together graphically using the head-to-tail method or mathematically using component addition to determine a vector sum or resultant vector. This vector can then be resolved into components and analyzed. Procedure: For each problem, vectors A, B and C are shown. 1) Sketch the head-to-tail addition of A+B+C on the empty grid, labeling each vector. 2) Draw and label the resultant (R) on the grid. 3) Complete the table by recording the x and y components for vectors A, B, and C. Use a positive sign (+) to indicate East or North; use a negative (-) to indicate a West or South. 4) Sum the components to determine the components of the resultant. Record the magnitude and direction of each component of the resultant. Use a positive sign (+) to indicate East or North; use a negative (-) to Indicate a West or South. 5) Verify your work. The resultant drawn on the grid should have the same components as shown in the table. If not, carefully repeat steps 1-4 to find your error. 6) Use the Pythagorean theorem and SOH CAH TOA to determine the magnitude and direction of R. a+ b'= c

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4:16 ull? Problem 3: Right-left Up-down E-W N-S Vector Components Components Magnitude of R (Pythagorean theorem): a'+ b = c? B Direction of R (SOH CAH TOA):
Transcribed Image Text:4:16 ull? Problem 3: Right-left Up-down E-W N-S Vector Components Components Magnitude of R (Pythagorean theorem): a'+ b = c? B Direction of R (SOH CAH TOA):
4:16 ull? Objective: To develop understanding of vectors by analyzing vector quantities and by addition of vectors using both graphical and mathematical methods. Background: A single vector may be analyzed by resolving the vector into horizontal (x) and vertical (y) components. This information then allows calculation of the magnitude (via Pythagorean Theorem) and angle (via trigonometry) of the original vector. Two or more vectors can be added together graphically using the head-to-tail method or mathematically using component addition to determine a vector sum or resultant vector. This vector can then be resolved into components and analyzed. Procedure: For each problem, vectors A, B and C are shown. 1) Sketch the head-to-tail addition of A+ B +Con the empty grid, labeling each vector. 2) Draw and label the resultant (R) on the grid. 3) Complete the table by recording the x and y components for vectors A, B, and C. Use a positive sign (+) to indicate East or North; use a negative (-) to indicate a West or South. 4) Sum the components to determine each component of the resultant. Use a positive sign (+) to indicate East or North; use a negative (-) to Indicate a West or South. ocomponents of the resultant. Record the magnitude and direction of 5) Verify your work. The resultant drawn on the grid should have the same components as shown in the table. If not, carefully repeat steps 1-4 to find your error. 6) Use the Pythagorean theorem and SOH CAH TOA to determine the magnitude and direction of R. a + b = c? Problem 1:
Transcribed Image Text:4:16 ull? Objective: To develop understanding of vectors by analyzing vector quantities and by addition of vectors using both graphical and mathematical methods. Background: A single vector may be analyzed by resolving the vector into horizontal (x) and vertical (y) components. This information then allows calculation of the magnitude (via Pythagorean Theorem) and angle (via trigonometry) of the original vector. Two or more vectors can be added together graphically using the head-to-tail method or mathematically using component addition to determine a vector sum or resultant vector. This vector can then be resolved into components and analyzed. Procedure: For each problem, vectors A, B and C are shown. 1) Sketch the head-to-tail addition of A+ B +Con the empty grid, labeling each vector. 2) Draw and label the resultant (R) on the grid. 3) Complete the table by recording the x and y components for vectors A, B, and C. Use a positive sign (+) to indicate East or North; use a negative (-) to indicate a West or South. 4) Sum the components to determine each component of the resultant. Use a positive sign (+) to indicate East or North; use a negative (-) to Indicate a West or South. ocomponents of the resultant. Record the magnitude and direction of 5) Verify your work. The resultant drawn on the grid should have the same components as shown in the table. If not, carefully repeat steps 1-4 to find your error. 6) Use the Pythagorean theorem and SOH CAH TOA to determine the magnitude and direction of R. a + b = c? Problem 1:
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