Practice: Vector F is 65 m long, directed 30.5° below the positive x-axis. (a) Find the x-component, Fx. (b) Find the y-component, Fy.

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Review of Vectors vs. Scalars | 2 mins | 0 completed | Learn |

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Vectors in 3D |

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Concept #1: Doing Math with Vectors in any Quadrant (More Trig)

Practice: Vector F is 65 m long, directed 30.5° below the positive x-axis. (a) Find the x-component, Fx. (b) Find the y-component, Fy.

Practice: The vector A represented is by the pair of components A_{x} = -77 cm , A_{y} = 36 cm. **(a)** Find the magnitude of vector A. **(b)** Find the absolute angle of this vector.

Practice: A small helicopter travels 225 m across a city in a direction 53.1° south of east. What are the components of the helicopter’s trip?

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Two vectors A and B have (x, y) components of (0, 1) and (-1, 3) respectively. What are the components of the sum of these two vectors?
A) (1,4)
B) (-1,2)
C) (1,2)
D) (-1,4)

A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, then 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point .(a) Find the magnitude of the third leg of the journey.(b) Find the direction of the third leg of the journey.

A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

PRACTICE: A velocity vector 41° below the positive x-axis has a y-component of −31 m/s. What is the value of its x-component?

Three vectors are shown in Fig. 3-38. 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 x-axis.

For the vectors given in the figure, determine(a) A - B + C(b) A + B - C(c) C - A - B

A warehouse worker pushes a crate along the floor by a force of 10 N that points downward at an angle of 45° below the horizontal.(a) Find the horizontal component of the force.(b) Find the vertical component of the force.

Consider a particle with initial velocity v that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis.(a) What is the x component vx of v ? Express your answer in meters per second.(b) What is the y component vy of v ? Express your answer in meters per second.

V is a vector 24.8 units in magnitude and points an angle of 23.4° above the negative axis.(a) Sketch this vector.(b) Calculate Vx and Vy.(c) Use Vx and Vy to obtain (again) the magnitude of V. [ Note: Part (c) is a good way to check if you've resolved your vector correctly.](d) Use Vx and Vy to obtain (again) the direction of V.

Vector A has y-component Ay = +15.0 m and makes an angle of 32.0° counterclockwise from the +y-axis.(a) What is the x-component of A?(b) What is the magnitude of A?

You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates ( −140 m, 30 m ). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and −70), then ( −20 and cy), then (−60 and −70). What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

I start walking. The 1st leg of my trip I walk dA = 105 m at θA = 24° south of east. The 2nd leg of my trip I walk dB = 65 m at θB = 28° north of east. On my final leg I walk dC = 95 m at θC = 63° north of west. Take east to be the +x direction and north to be the +y direction.Part (a) Write an expression for the x component of the final displacement in terms of the given quantities.Part (b) Write an expression for the y component of the final displacement in terms of the given quantities.Part (c) What is the magnitude of my displacement vector (in meters) as measured from the origin?Part (d) What is the angle of my displacement vector as measured counterclockwise from the +x-axis (East)?

A student bikes to school by traveling first dN = 0.900 miles north, then dW = 0.300 miles west, and finally dS = 0.200 miles south.Finally, find ϕ, the angle north of west of the path followed by the bird.Express your answer numerically in degrees.

You leave the airport in College Station and fly 24.0 km in a direction 34.0° south of east. You then fly 46.0 km m kmdue north.How far must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?In what direction?

Two forces, F1 and F2, act at a point, as shown in the picture. (Fiqure 1) F1 has a magnitude of 8.80 N and is directed at an angle of α-65.0° above the negative x axis in the second quadrant. F2 has a magnitude of 5.40 N and is directed at an angle of β = 53.3° below the negative x axis in the third quadrant. A) What is the x component Fx of the resultant force?B) What is the y component Fy of the resultant force?C) What is the magnitude F of the resultant force?D) What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

1. Find out the x-component and y-component of the following vectors:A = 15.0 cm; the vector is 30.00° north of west;B = 12.0 m; the vector is 55.00° north of east;C = 28.0 m/s; the vector is 40.00° south of west;D = 55.5 m/s2; the vector is 35.00° south of east.

Vector A is in the direction 34.0° clockwise from the −y-axis. The x-component of A is Ax = −16.0 m.(a) What is the y-component of A?(b) What is the magnitude of A?

For the vectors shown in the figure, determine B - 2A. Vector magnitudes are given in arbitrary units.

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