College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 1, Problem 57P

(a)

To determine

The components of C=A+B.

(a)

Expert Solution
Check Mark

Answer to Problem 57P

The components of C=A+B, are Cx=22_, and Cy=30_, magnitude of C is 37_, and direction is 53°_.

Explanation of Solution

Write the expression for the x component of C.

  Cx=Ax+Bx        (I)

Write the expression for the y component of C.

  Cy=Ay+By        (II)

Write the expression for the magnitude of C.

  C=Cx2+Cy2        (III)

Write the expression for the direction of C.

  θ=tan1(CyCx)        (IV)

Conclusion:

Substitute, 13.6 for Ax, and 8.55 for Bx in equation (I) to find Cx.

  Cx=13.6+8.55=22.2

Substitute, 6.34 for Ay, and 23.5 for By in equation (I) to find Cy.

  Cy=6.34+23.5=29.8

Substitute, 22.2 for Cx, and 29.8 for Cy in equation (III) to find the magnitude of vector C.

  C=(22.2)2+(29.8)2=37

Substitute, 22.2 for Cx, and 29.8 for Cy in equation (IV) to find the direction of vector C.

  θ=tan1(29.822.2)=53°

Therefore, the components of C=A+B, are Cx=22_, and Cy=30_, magnitude of C is 37_, and direction is 53°_.

(b)

To determine

The components of C=AB.

(b)

Expert Solution
Check Mark

Answer to Problem 57P

The components of C=AB, are Cx=5.05_, and Cy=17.6_, magnitude of C is 18_, and direction is 74°_.

Explanation of Solution

Write the expression for the x component of C.

  Cx=AxBx        (V)

Write the expression for the y component of C.

  Cy=AyBy        (VI)

Conclusion:

Substitute, 13.6 for Ax, and 8.55 for Bx in equation (V) to find Cx.

  Cx=13.68.55=5.05

Substitute, 6.34 for Ay, and 23.5 for By in equation (VI) to find Cy.

  Cy=6.3423.5=17.16

Substitute, 5.05 for Cx, and 17.2 for Cy in equation (III) to find the magnitude of vector C.

  C=(5.05)2+(17.2)2=18

Substitute, 5.05 for Cx, and 17.2 for Cy  in equation (IV) to find the direction of vector C.

  θ=tan1(17.165.05)=74°

Therefore, the components of C=AB, are Cx=5.05_, and Cy=17.6_, magnitude of C is 18_, and direction is 74°_.

(c)

To determine

The components of C=A+4B.

(c)

Expert Solution
Check Mark

Answer to Problem 57P

The components of C=A+4B, are Cx=47.8_, and Cy=100_, magnitude of C is 110_, and direction is 64°_.

Explanation of Solution

Write the expression for the x component of C.

  Cx=Ax+4Bx        (VII)

Write the expression for the y component of C.

  Cy=Ay+4By        (VIII)

Conclusion:

Substitute, 13.6 for Ax, and 8.55 for Bx in equation (VII) to find Cx.

  Cx=13.6+4(8.55)=47.8

Substitute, 6.34 for Ay, and 23.5 for By in equation (VIII) to find Cy.

  Cy=6.344(23.5)=100

Substitute, 47.8 for Cx, and 100 for Cy in equation (III) to find the magnitude of vector C.

  C=(47.8)2+(100)2=110

Substitute, 47.8 for Cx, and 100 for Cy in equation (IV) to find the direction of vector C.

  θ=tan1(10047.8)=64°

Therefore, the components of C=A+4B, are Cx=47.8_, and Cy=100_, magnitude of C is 110_, and direction is 64°_.

(b)

To determine

The components of C=A7B.

(b)

Expert Solution
Check Mark

Answer to Problem 57P

The components of C=A7B, are Cx=73.5_, and Cy=171_, magnitude of C is 190_, and direction is 67°_.

Explanation of Solution

Write the expression for the x component of C.

  Cx=Ax7Bx        (IX)

Write the expression for the y component of C.

  Cy=Ay7By        (X)

Conclusion:

Substitute, 13.6 for Ax, and 8.55 for Bx in equation (IX) to find Cx.

  Cx=13.67(8.55)=73.5

Substitute, 6.34 for Ay, and 23.5 for By in equation (X) to find Cy.

  Cy=6.347(23.5)=171

Substitute, 73.5 for Cx, and 171 for Cy in equation (III) to find the magnitude of vector C.

  C=(73.5)2+(171)2=190

Substitute, 73.5 for Cx, and 171 for Cy in equation (IV) to find the direction of vector C.

  θ=tan1(17173.5)=67°

Therefore, components of C=A7B, are Cx=73.5_, and Cy=171_, magnitude of C is 190_, and direction is 67°_.

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College Physics, Volume 1

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