FlipIt for College Physics (Algebra Version - Six Months Access)
FlipIt for College Physics (Algebra Version - Six Months Access)
17th Edition
ISBN: 9781319032432
Author: Todd Ruskell
Publisher: W.H. Freeman & Co
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Chapter 3, Problem 32QAP
To determine

(a)

The components of the vector A+B

Expert Solution
Check Mark

Answer to Problem 32QAP

The x component of the vector A+B is 13 units and its y component is 6 units.

Explanation of Solution

Given:

The components of the vectors A,B and C

  Ax=6Ay=9Bx=7By=3Cx=0Cy=6

Formula used:

If A+B=P, then the x component of P is given by,

  Px=Ax+Bx

And the y component of P is given by,

  Py=Ay+By

Calculation:

Substitute the given values of the variables in the formula and calculate the x component.

  Px=Ax+Bx=6+7=13

Substitute the given values of the variables in the formula and calculate the y component.

  Py=Ay+By=93=6

Conclusion:

The x component of the vector A+B is 13 units and its y component is 6 units.

To determine

(b)

The components of the vector A2C.

Expert Solution
Check Mark

Answer to Problem 32QAP

The x component of the vector A2C is 6 units and the y component is 21 units.

Explanation of Solution

Given:

The components of the vectors A,B and C

  Ax=6Ay=9Bx=7By=3Cx=0Cy=6

Formula used:

If A2C=Q, then the x component of the vector Q is given by,

  Qx=Ax2Cx

The y component is given by,

  Qy=Ay2Cy

Calculation:

Substitute the given values of the variables in the formula and calculate the x component.

  Qx=Ax2Cx=62×0=6

Substitute the given values of the variables in the formula and calculate the y component.

  Qy=Ay2Cy=92×6=21

Conclusion:

The x component of the vector A2C is 6 units and the y component is 21 units.

To determine

(c)

The components of the vector A+BC.

Expert Solution
Check Mark

Answer to Problem 32QAP

The x component of the vector A+BC is 13 units and the y component is 12 units.

Explanation of Solution

Given:

The components of the vectors A,B and C

  Ax=6Ay=9Bx=7By=3Cx=0Cy=6

Formula used:

If A+BC=R, then, the x component of the vector R is given by,

  Rx=Ax+BxCx

The y component is given by,

  Ry=Ay+ByCy

Calculation:

Substitute the given values of the variables in the formula and calculate the x component.

Rx=Ax+BxCx=6+70=13

Substitute the given values of the variables in the formula and calculate the y component.

Ry=Ay+ByCy=9+36=12

Conclusion:

The x component of the vector A+BC is 13 units and the y component is 12 units.

To determine

(d)

The components of the vector A+12B3C.

Expert Solution
Check Mark

Answer to Problem 32QAP

The x component of the vector A+12B3C is 9.5 units and the y component is 25.5 units.

Explanation of Solution

Given:

The components of the vectors A,B and C

  Ax=6Ay=9Bx=7By=3Cx=0Cy=6

Formula used:

If A+12B3C=S, then its x component is given by,

  Sx=Ax+12Bx3Cx

The y component is given by,

  Sy=Ay+12By3Cy

Calculation:

Substitute the given values of the variables in the formula and calculate the x component of the vector A+12B3C.

  Sx=Ax+12Bx3Cx=6+12×73×0=9.5

Substitute the given values of the variables in the formula and calculate the y component of the vector A+12B3C.

  Sy=Ay+12By3Cy=9+12336=25.5

Conclusion:

The x component of the vector A+12B3C is 9.5 units and the y component is 25.5 units.

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