Vector A has a negative x component 3.05 units in length and a positive y component 1.95 units in length. (a) Determine an expression for A in unit-vector notation. (b) Determine the magnitude and direction of A. (c) What vector B, when added to vector A, gives a resultant vector with no x component and a negative y component 3.63 units in length?

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11th Edition
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Chapter1: Units, Trigonometry. And Vectors
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Vector A has a negative x component 3.05 units in length and a positive y component 1.95 units in length.
(a) Determine an expression for A in unit-vector notation.
(b) Determine the magnitude and direction of A.
(c) What vector B, when added to vector A, gives a resultant vector with no x component and a negative y component 3.63 units in length?
Step 1
The component description determines the unit-vector expression for vector A. Its magnitude and direction are determined from its components. The vector B will be
determined from the description of the resultant vector R along with the known components of A.
Step 3
(a) We are given Ax
A = A
Step 2
Determine the unit-vector notation for A using its given components. We know the components of the resulting vector R
=
A + B, and from this we can determine the vector B
A
Axî + A,ĵ = (-3.05
= -3.05
=
=
€
-3.05
0
Step 4
(b) The magnitude of A is given by the following equation.
2
A₂²2² + Ay²
X
X
1.95
-3.05 unit(s) and Ay = 1.95
-3.05 +1.95
3.05 unit(s))² + 1.95
Co
1.95 unit(s). We have the following expression for A in unit-vector notation.
1.95 ĵ) unit(s)
1.95 unit(s))² = 3.60
3.62 unit(s)
Step 5
We find the angle using the following equations.
tan 0 Y =
Av
Ax
unit(s)
unit(s)
-3.06
Enter a number.
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.,
tan ¹(-32.59
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.) = = 147.41
The response you submitted has the wrong sign.º
X
Transcribed Image Text:Vector A has a negative x component 3.05 units in length and a positive y component 1.95 units in length. (a) Determine an expression for A in unit-vector notation. (b) Determine the magnitude and direction of A. (c) What vector B, when added to vector A, gives a resultant vector with no x component and a negative y component 3.63 units in length? Step 1 The component description determines the unit-vector expression for vector A. Its magnitude and direction are determined from its components. The vector B will be determined from the description of the resultant vector R along with the known components of A. Step 3 (a) We are given Ax A = A Step 2 Determine the unit-vector notation for A using its given components. We know the components of the resulting vector R = A + B, and from this we can determine the vector B A Axî + A,ĵ = (-3.05 = -3.05 = = € -3.05 0 Step 4 (b) The magnitude of A is given by the following equation. 2 A₂²2² + Ay² X X 1.95 -3.05 unit(s) and Ay = 1.95 -3.05 +1.95 3.05 unit(s))² + 1.95 Co 1.95 unit(s). We have the following expression for A in unit-vector notation. 1.95 ĵ) unit(s) 1.95 unit(s))² = 3.60 3.62 unit(s) Step 5 We find the angle using the following equations. tan 0 Y = Av Ax unit(s) unit(s) -3.06 Enter a number. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully., tan ¹(-32.59 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.) = = 147.41 The response you submitted has the wrong sign.º X
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