Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
1st Edition
ISBN: 9781305259836
Author: Debora M. Katz
Publisher: Cengage Learning
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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

Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics

Ch. 3 - Prob. 6PQCh. 3 - Prob. 7PQCh. 3 - The layout of the town of Popperville is a...Ch. 3 - Prob. 9PQCh. 3 - Prob. 10PQCh. 3 - Prob. 11PQCh. 3 - Prob. 12PQCh. 3 - In Chapter 5, you will study a very important...Ch. 3 - Refer to the situation described in Problem 14....Ch. 3 - Vector A has a magnitude of 4.50 m and makes an...Ch. 3 - Miguel, an Ultimate Frisbee player, is running...Ch. 3 - A baseball diamond consists of four plates...Ch. 3 - Prob. 19PQCh. 3 - Prob. 20PQCh. 3 - Two aircraft approaching an aircraft carrier are...Ch. 3 - Prob. 22PQCh. 3 - A truck driver delivering office supplies downtown...Ch. 3 - Prob. 24PQCh. 3 - Carolyn rides her bike 40.0 south of west for 5.40...Ch. 3 - Prob. 26PQCh. 3 - Prob. 27PQCh. 3 - Prob. 28PQCh. 3 - Prob. 29PQCh. 3 - Prob. 30PQCh. 3 - Prob. 31PQCh. 3 - Prob. 32PQCh. 3 - Prob. 33PQCh. 3 - Prob. 34PQCh. 3 - A firecracker explodes into four equal pieces...Ch. 3 - Prob. 36PQCh. 3 - Prob. 37PQCh. 3 - Prob. 38PQCh. 3 - Prob. 39PQCh. 3 - Figure P3.40 shows a map of Grand Canyon National...Ch. 3 - Prob. 41PQCh. 3 - The same vectors that are shown in Figure P3.6 are...Ch. 3 - A supertanker begins in Homer, Alaska, sails 125...Ch. 3 - A Three vectors are shown in Figure P3.44, but...Ch. 3 - A vector A=(5.20i3.70j) m and a vector...Ch. 3 - Prob. 46PQCh. 3 - Prob. 47PQCh. 3 - Prob. 48PQCh. 3 - An airplane leaves city A and flies a distance d1...Ch. 3 - An aircraft undergoes two displacements. If the...Ch. 3 - The resultant vector R=2AB2C has zero magnitude....Ch. 3 - A Three vectors all have the same magnitude. The...Ch. 3 - The two-dimensional vectors A and B both have...Ch. 3 - Prob. 54PQCh. 3 - Two birds begin next to each other and then fly...Ch. 3 - Prob. 56PQCh. 3 - General Problems 57. G A spider undergoes the...Ch. 3 - Peter throws a baseball through a houses window....Ch. 3 - Prob. 59PQCh. 3 - Prob. 60PQCh. 3 - Prob. 61PQCh. 3 - A glider aircraft initially traveling due west at...Ch. 3 - What are the magnitude and direction of a vector...Ch. 3 - Prob. 64PQCh. 3 - Prob. 65PQCh. 3 - Prob. 66PQCh. 3 - Prob. 67PQCh. 3 - Prob. 68PQCh. 3 - Prob. 69PQCh. 3 - Prob. 70PQCh. 3 - Vector F is proportional to vector A such that...Ch. 3 - Prob. 72PQCh. 3 - Prob. 73PQCh. 3 - Problems 74 and 75 are paired. 74. N A classroom...Ch. 3 - Prob. 75PQ
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