College Physics
College Physics
5th Edition
ISBN: 9781260486841
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 2, Problem 26P

(a)

To determine

The x and y components of b.

(a)

Expert Solution
Check Mark

Answer to Problem 26P

The x and y components of b are 7 and 2 respectively.

Explanation of Solution

The magnitude of b is 7.1 and it is in direction 14° the +x axis.

Write the expression for x component of b.

  bx=bcosθ        (I)

Here, b is the magnitude of b, and θ is the angle inclined by b with x axis.

Write the expression for y component of b.

  by=bsinθ        (II)

Conclusion:

Substitute, 7.1 for b, 14° for θ in equation (I) to find the x component of b.

  bx=(7.1)cos(14°)=7.1×0.970=6.9

Substitute, 7.1 for b, 14° for θ in equation (II) to find the y component of b.

  by=(7.1)sin(14°)=7.1×0.24=1.7

Hence the vector representation of b is.

  b=bxi^+byj^=6.9i^+1.7j^

Conclusion:

Therefore, the x and y components of b are 6.9 and 1.7 respectively.

(b)

To determine

The magnitude and direction of c.

(b)

Expert Solution
Check Mark

Answer to Problem 26P

The magnitude of c is 6.94_ and direction of c 74.9°_.

Explanation of Solution

The x component of c is 1.8, and y component of c is 6.7.

Write the vector expression for c.

  c=cxi^+cyj^        (III)

Here, cx is the x component of c, and cy is the y component of c.

Write the equation to find the magnitude of c.

  c=cx2+cy2        (IV)

Write the expression for the direction of c.

  θ=tan1(cycx)        (V)

Conclusion:

Substitute, 1.8 for cx, and 6.7 for cy in equation (IV) to find the magnitude of c.

  c=(1.8)2+(6.7)2=6.94

Substitute, 1.8 for cx, and 6.7 for cy in equation (V) to find the direction of c.

  θ=tan1(6.71.8)=74.9°

Therefore, the magnitude of c is 6.94_ and direction of c 74.9°_.

(c)

To determine

The magnitude and direction of c+b.

(c)

Expert Solution
Check Mark

Answer to Problem 26P

The magnitude of c+b is 7.14_, and direction of c+b is .

Explanation of Solution

Let the sum of vector c and b be vector a.

Write the vector expression for a.

  a=c+baxi^+ayj^=(cxi^+cyj^)+(bxi^+byj^)        (VI)

Write the expression for finding the magnitude of a.

  a=ax2+ay2        (VII)

Write the expression for finding the direction of a.

  θ=tan1(ayax)        (VIII)

Conclusion:

Substitute, 6.9 for bx, 1.7 for by, 1.8 for cx, and 6.7 for cy in equation (VI).

  axi^+ayj^=(1.8i^+6.7yj^)+(6.9i^+1.7j^)=5.1i^5j^        (IX)

Substitute, 5.1 for ax, and 5 for ay in equation (VII) to find the magnitude of a.

  a=(5.1)2+(5)2=7.14

Substitute, 5.1 for ax, and 5 for ay in equation (VIII) to find the direction of a.

  θ=tan1(55.1)=

Therefore, the magnitude of c+b is 7.14_, and direction of c+b is .

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Chapter 2 Solutions

College Physics

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