EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
1st Edition
ISBN: 9780100546714
Author: Katz
Publisher: YUZU
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Chapter 3, Problem 33PQ

(a)

To determine

Component form of vector A.

(a)

Expert Solution
Check Mark

Answer to Problem 33PQ

Component form of vector A is 4i^2j^.

Explanation of Solution

Write the x-component of vector A.

    Ax=4.00units

Here, Ax is the x-component of vector A.

Write the y-component of vector A.

    Ay=2.00units

Here, Ay is the y-component of vector A.

Write the expression for component form of vector A.

  A=Axi^+Ayj^

Here, i^ is the unit normal vector in x-direction and j^ is the unit normal vector in y-direction.

Conclusion:

Substitute 4.00units for Ax and 2.00units for Ay in the above equation for the component form of vector A.

    A=(4.00units)i^+(2.00units)j^=(4.00units)i^(2.00units)j^

Therefore, the component form of vector A is (4.00units)i^(2.00units)j^.

(b)

To determine

Magnitude and direction of vector A.

(b)

Expert Solution
Check Mark

Answer to Problem 33PQ

Magnitude is 20units and directed at 26.56° with respect to negative x direction.

Explanation of Solution

Write the expression to find the magnitude of vector A.

  A=Ax2+Ay2

Here, A is the magnitude of vector A.

Since both Ax and Ay are negative, A lies in the third quadrant. Write the equation to find the direction of A with respect to –x axis.

    θ=tan1(AyAx)

Here, θ is the direction of A with respect to –x axis.

Conclusion:

Substitute 4.00units for Ax and 2.00units for Ay in the equation for A.

    A=(4.00units)2+(2.00units)2=20units=4.47units

Substitute 4.00units for Ax and 2.00units for Ay in the equation for θ.

  θ=tan1(2.00units4.00units)=tan1(0.5)=26.56°

Thus, the magnitude is 4.47units and directed at 26.56° with respect to negative x direction.

The angle from positive x axis given by

  θ=180°+26.56°=206.56°207°

Therefore, the magnitude and direction of the vector is 4.47units and 207°.

(c)

To determine

Identify B such that on addition with A gives a resultant with 6.00units of x-component and no y-component.

(c)

Expert Solution
Check Mark

Answer to Problem 33PQ

Vector B is (2.00units)i^+(2.00units)j^.

Explanation of Solution

Write the relation between Ax,Bx and Cx.

  Bx=CxAx

Here, Cx is the x-component of C and Bx is the x-component of B.

Write the relation between Ay,By and Cy.

  By=CyAy

Here, Cy is the y-component of C and By is the y-component of B.

Write the expression for component form of vector B.

  B=Bxi^+Byj^

Conclusion:

Substitute 6.00units for Cx and 4.00units for Ax in equation in the equation for Bx.

    Bx=6.00units(4.00units)=2.00units

Substitute 0.00units for Cy and 2.00units for Ay the equation for By.

  By=0.00units(2.00units)=2.00units

Substitute 2.00units for Bx and 2.00units for By in the equation for B.

    B=(2.00units)i^+(2.00units)j^

Therefore, the vector B is (2.00units)i^+(2.00units)j^.

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Chapter 3 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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