Vectors A and B have the same magnitude. Furthermore, the angle 0A that A makes with the positive y-axis is equal to the angle 0B that B makes with the negative y-axis. The magnitude of C is Asin 0A (the sign or direction is not accounted for, this is just the "length." You will need to supply the appropriate sign to account for the direction). The sketch below shows the orientations of the vectors. Which of the following is the correct expression for the resultant vector R (recall that the resultant vector R, in this case, is sum of vectors A, B, and C)? +y↑ OB

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Chapter1: Units, Trigonometry. And Vectors
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Question 5
Vectors A and B have the same magnitude. Furthermore, the angle 0 A that A makes with the positive y-axis
is equal to the angle OB that B makes with the negative y-axis. The magnitude of C is Asin 0A (the sign
or direction is not accounted for, this is just the "length." You will need to supply the appropriate sign to
account for the direction). The sketch below shows the orientations of the vectors. Which of the following
is the correct expression for the resultant vector R (recall that the resultant vector R, in this case, is sum of
vectors A, B, and C)?
+y↑
OB
(Hint: First, draw the components of all the vectors, make sure the components are pointing in the correct
directions and label them generically-for example, Ag, Ay, Bg, By, etc. Second, use the relationship among
the vectors to write them all in common terms, for example, it is stated that the magnitude of C is Asin 0A.
Use this as a hint and write the components of B in terms of components of A, this can be done because the
magnitude of A and B are equal; in addition, 0A = 0B. But there is a difference between A and B, what
is it?-Look at the figure. If everything is done correctly when drawing the components and labelling them
appropriately while keeping their relationships in mind, the problem can be solved pictorially.)
%3D
a) R= A cos 0AÎ + 2A sin 0Aâŷ
b) Ř= /A² + B² +C?ê+ \/A3 + B +Czŷ
%3D
c) R= Asin 0A£
d) R= C = -A sin 0AÎ
%3D
Transcribed Image Text:Question 5 Vectors A and B have the same magnitude. Furthermore, the angle 0 A that A makes with the positive y-axis is equal to the angle OB that B makes with the negative y-axis. The magnitude of C is Asin 0A (the sign or direction is not accounted for, this is just the "length." You will need to supply the appropriate sign to account for the direction). The sketch below shows the orientations of the vectors. Which of the following is the correct expression for the resultant vector R (recall that the resultant vector R, in this case, is sum of vectors A, B, and C)? +y↑ OB (Hint: First, draw the components of all the vectors, make sure the components are pointing in the correct directions and label them generically-for example, Ag, Ay, Bg, By, etc. Second, use the relationship among the vectors to write them all in common terms, for example, it is stated that the magnitude of C is Asin 0A. Use this as a hint and write the components of B in terms of components of A, this can be done because the magnitude of A and B are equal; in addition, 0A = 0B. But there is a difference between A and B, what is it?-Look at the figure. If everything is done correctly when drawing the components and labelling them appropriately while keeping their relationships in mind, the problem can be solved pictorially.) %3D a) R= A cos 0AÎ + 2A sin 0Aâŷ b) Ř= /A² + B² +C?ê+ \/A3 + B +Czŷ %3D c) R= Asin 0A£ d) R= C = -A sin 0AÎ %3D
Expert Solution
Step 1

Magnitude of vector A= Magnitude of vector BLet this magnitude = F θA = θA = θ

 

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