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Find the sum of two displacement vectors A and B lying in the xy-plane and given by A- (1.201 + 2.15j) m and B- (6.0oi + (-5.60)j) m. SOLUTION Conceptualize You can conceptualize the situation by drawing the vectors on graph paper. Draw an approximation of the expected resultant vector. Categorize We categorize this example as a simple substitution problem. Comparing this expression for A with the general expression A - Ai + Aj+ AK, we see that A, - 1.20 m, A, - 2.15 m, and A,-0 m. Likewise, B- B, -0 m. We can use a two-dimensional approach because there are no z-components. m, 8, - [ m, Use the following equation to obtain the resultant vector R: R-A B-( + 6.00)i m + (2.15 + Evaluate the components of R (in m): R. Use the following equation to find the magnitude of R (in m): R-V (R.) + (R- m Find the direction of R from the following equation: tan(0) - Your calculator likely gives the answer -25.6° for e- tan(-0.479). This answer is correct if we interpret it to mean 25.6° clockwise from the x-axis. Our standard form has been quote the angles measured counterclockwise from the +x-axis, and that angle fo vector (in degrees) is - EXERCISE Find the difference of two vectors A- B lying in the xy-plane and given by the following notation. (Enter the direction in degrees counterclockwise from the +x-axis.) A- 1.00i + 5.75j B- 3.00i + 3.75j Hint • counterclockwise from the +x-axis

Find the sum of two displacement vectors A and B lying in the xy-plane and given by A- (1.201 + 2.15j) m and B- (6.0oi + (-5.60)j) m. SOLUTION Conceptualize You can conceptualize the situation by drawing the vectors on graph paper. Draw an approximation of the expected resultant vector. Categorize We categorize this example as a simple substitution problem. Comparing this expression for A with the general expression A - Ai + Aj+ AK, we see that A, - 1.20 m, A, - 2.15 m, and A,-0 m. Likewise, B- B, -0 m. We can use a two-dimensional approach because there are no z-components. m, 8, - [ m, Use the following equation to obtain the resultant vector R: R-A B-( + 6.00)i m + (2.15 + Evaluate the components of R (in m): R. Use the following equation to find the magnitude of R (in m): R-V (R.) + (R- m Find the direction of R from the following equation: tan(0) - Your calculator likely gives the answer -25.6° for e- tan(-0.479). This answer is correct if we interpret it to mean 25.6° clockwise from the x-axis. Our standard form has been quote the angles measured counterclockwise from the +x-axis, and that angle fo vector (in degrees) is - EXERCISE Find the difference of two vectors A- B lying in the xy-plane and given by the following notation. (Enter the direction in degrees counterclockwise from the +x-axis.) A- 1.00i + 5.75j B- 3.00i + 3.75j Hint • counterclockwise from the +x-axis

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter3: Vectors
Section: Chapter Questions
Problem 65PQ
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The Sum of Two Vectors Find the sum of two displacement vectors A and B lying in the xy-plane and given by A = (1.20î + 2.15j) m and B = (6.0oi + (-5.60)j) m. SOLUTION Conceptualize You can conceptualize the situation by drawing the vectors on graph paper. Draw an approximation of the expected resultant vector. Categorize We categorize this example as a simple substitution problem. Comparing this expression for A with the general expression A = Ai + Aj+ Ak, we see that A, = 1.20 m, A, = 2.15 m, and A, = 0 m. Likewise, B, = B, = 0 m. We can use a two-dimensional approach because there are no z-components. ]m, 8, = [ m, and Use the following equation to obtain the resultant vector R: R-A+B = ( + 6.00)i m + (2.15 + Evaluate the components of R (in m): m R- m Use the following equation to find the magnitude of R (in m): R = v (R)? + (R,)? - Find the direction of R from the following equation: tan(e) = Your calculator likely gives the answer -25.6° for e - tan(-0.479). This answer is correct if we interpret it to mean 25.6° clockwise from the x-axis. Our standard form has been quote the angles measured counterclockwise from the +x-axis, and that angle for this vector (in degrees) is e- EXERCISE Find the difference of two vectors A - B lying in the xy-plane and given by the following notation. (Enter the direction in degrees counterclockwise from the +x-axis.) 1.00i + 5.7 B = 3.00i + 3.75j Hint ° counterclockwise from the +x-axis
Transcribed Image Text:The Sum of Two Vectors Find the sum of two displacement vectors A and B lying in the xy-plane and given by A = (1.20î + 2.15j) m and B = (6.0oi + (-5.60)j) m. SOLUTION Conceptualize You can conceptualize the situation by drawing the vectors on graph paper. Draw an approximation of the expected resultant vector. Categorize We categorize this example as a simple substitution problem. Comparing this expression for A with the general expression A = Ai + Aj+ Ak, we see that A, = 1.20 m, A, = 2.15 m, and A, = 0 m. Likewise, B, = B, = 0 m. We can use a two-dimensional approach because there are no z-components. ]m, 8, = [ m, and Use the following equation to obtain the resultant vector R: R-A+B = ( + 6.00)i m + (2.15 + Evaluate the components of R (in m): m R- m Use the following equation to find the magnitude of R (in m): R = v (R)? + (R,)? - Find the direction of R from the following equation: tan(e) = Your calculator likely gives the answer -25.6° for e - tan(-0.479). This answer is correct if we interpret it to mean 25.6° clockwise from the x-axis. Our standard form has been quote the angles measured counterclockwise from the +x-axis, and that angle for this vector (in degrees) is e- EXERCISE Find the difference of two vectors A - B lying in the xy-plane and given by the following notation. (Enter the direction in degrees counterclockwise from the +x-axis.) 1.00i + 5.7 B = 3.00i + 3.75j Hint ° counterclockwise from the +x-axis
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