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3. Vectors

Adding Vectors by Components

3. Vectors

Adding Vectors by Components

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Vector Addition By Components

Vector Addition By Components

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Anderson Video - Displacement Vectors and Adding Vectors

Anderson Video - Displacement Vectors and Adding Vectors

Anderson Video - Adding Vector Components

Anderson Video - Adding Vector Components

Anderson Video - Adding Vectors Example

Anderson Video - Adding Vectors Example

Anderson Video - Adding Vector Components Example

Anderson Video - Adding Vector Components Example

Vectors - Finding the components of a vector

Vectors - Finding the components of a vector

Scott Teaches Physics

Adding Vectors: How to Find the Resultant of Three or More Vectors

Adding Vectors: How to Find the Resultant of Three or More Vectors

Physics Vector Addition (Algebraic)

Physics Vector Addition (Algebraic)

Physicshelp Canada

Vector Component Addition and Subtraction

Vector Component Addition and Subtraction

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Practice this topic

Multiple Choice

\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}

\overset{⇀}{B} = - 7.0 \hat{i}

\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}

. What is the direction of

\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}

? Express your answer in degrees counter clockwise from the positive x axis.

Multiple Choice

\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}

\overset{⇀}{B} = - 7.0 \hat{i}

\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}

. What is the magnitude of

\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}

Textbook Question

A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of (d) the vector difference B - A

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of (c) the vector difference A - B

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of (a) the vector sum A + B

Textbook Question

FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving? Give the direction as an angle below the negative x-axis.

Textbook Question

A position vector in the first quadrant has an x-component of 6 m and a magnitude of 10 m. What is the value of its y-component?

Textbook Question

A velocity vector 40 degrees below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

Textbook Question

The bacterium E. coli is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. FIGURE P3.42 shows the trajectory of an E. coli as it moves from point A to point E. What are the magnitude and direction of the bacterium's average velocity for the entire trip?

Textbook Question

FIGURE P3.26 shows vectors A and B. Find D = 2A ＋B Write your answer in component form.

Textbook Question

Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 30 mi she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to get her. What is Ward's displacement vector? Give your answer (a) in component form, using a coordinate system in which the y-axis points north, and (b) as a magnitude and direction.

Textbook Question

While vacationing in the mountains you do some hiking. In the morning, your displacement is Sₘₒᵣₙᵢₙ₉ = (2000 m, east) ＋ (3000 m, north) ＋(200 m, vertical). Continuing on after lunch, your displacement is Sₐբₜₑᵣₙₒₒₙ = (1500 m, west) ＋ (2000 m, north) ─ (300 m, vertical). b. What is the magnitude of your net displacement for the day?

Textbook Question

While vacationing in the mountains you do some hiking. In the morning, your displacement is Sₘₒᵣₙᵢₙ₉ = (2000 m, east) ＋ (3000 m, north) ＋(200 m, vertical). Continuing on after lunch, your displacement is Sₐբₜₑᵣₙₒₒₙ = (1500 m, west) ＋ (2000 m, north) ─ (300 m, vertical). a. At the end of the hike, how much higher or lower are you compared to your starting point?

Textbook Question

A runner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. The runner starts at (x,y) = (50m, 0m) and runs 2.5 times around the track in aclockwise direction. What is his displacement vector? Give your answer as a magnitude and direction.

Textbook Question

A crate, seen from above, is pulled with three ropes that have the tensions shown in FIGURE P3.44. Tension is a vector directed along the rope, measured in newtons (abbreviated N). Suppose the three ropes are replaced with a single rope that has exactly the same effect on the crate. What is the tension in this rope? Write your answer in component form using unit vectors.

Textbook Question

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (b) r = (-2.0i - 1.0j) cm

Textbook Question

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (a) B = -4.0i + 4.0j

Textbook Question

Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. (c) v = (14i - 11j) m/s

Textbook Question

Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. (a) A = 3.0i + 7.0j

Textbook Question

Let A = (3.0 m, 20° south of east), B = (2.0 m, north), and C = (5.0 m, 70° south of west). c. Find the magnitude and the direction of D = A＋B＋C.

Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (a) Write vector F in component form.

Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B. (c) What are the magnitude and director of vector E?

Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (c) What are the magnitude and director of vector C?

Textbook Question

Four forces are exerted on the object shown in FIGURE P3.45. (Forces are measured in newtons, abbreviated N.) The net force on the object is Fₙₑₜ = F₁ + F₂ + F₃ + F₄ = 4.0î N. What are (a) F₃ and (b) F₄? Give your answers in component form.

Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (c) What are the magnitude and director of vector F?

Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (a) Write vector C in component form.

Textbook Question

(II) For the vectors shown in Fig. 3–41, determine

(b) 2 A (→ above A) ― 3 B (→ above B) + 2 C (→ above C) , and

Textbook Question

(II) Three vectors are shown in Fig. 3–41. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the +𝓍 axis.

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Textbook Question

(II) Figure 3–39 shows two vectors, A (→ above A) and B (→ above B) , whose magnitudes are A = 6.8 units and B = 5.5 units. Determine C (→ above C) if

(a) C(→ above C) = A (→ above A) + B (→ above B) ,

Give the magnitude and direction for each.

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Textbook Question

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (b) Draw a coordinate system and on it show vectors A, B, and F

Textbook Question

c. Use components to determine the magnitude and direction of G = E＋F.

Textbook Question

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (d) a = (20i + 10j) m/s^2

Textbook Question

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. a. From 8:00 to 8:20 a.m.

Textbook Question

FIGURE P3.46 shows four electric charges located at the corners of a rectangle. Like charges, you will recall, repel each other while opposite charges attract. Charge B exerts a repulsive force (directly away from B) on charge A of 3.0 N. Charge C exerts an attractive force (directly toward C) on charge A of 6.0 N. Finally, charge D exerts an attractive force of 2.0 N on charge A. Assuming that forces are vectors, what are the magnitude and direction of the net force Fₙₑₜ exerted on charge A?

Textbook Question

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. b. From 8:00 to 9:00 a.m.

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