Vector A is 4 N pointed at 60 degrees. Vector B is 6 N pointed at 120 degrees. Find the magnitude...
Question:
Vector A is 4 N pointed at 60 degrees. Vector B is 6 N pointed at 120 degrees. Find the magnitude and direction of the resultant vector. Draw to scale a diagram depicting these forces and the resultant force.
Vector Addition
Vector addition can be done graphically or algebraically. Graphically, vectors can be added by drawing them as arrows on a Cartesian coordinate system. Algebraically, they can be added by doing a component-wise addition, where the components are combined independently.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer1.) The given vectors may be written in component form as
$$\vec{V} = V \cos \theta \hat{i}+ V \sin \theta \hat{j} \ \ \ \text{ [Equation 1]} $$
wh...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Vectors in Math: Addition, Subtraction, Division & Multiplication
from
Chapter 9 / Lesson 11
476
Vectors represent a magnitude in a specific direction, and follow similar rules as numbers, just with a couple of extra steps. Learn how vectors act with addition, subtraction, multiplication, and division.
Related to this Question
- Two forces, vector F_1 and vector F_2, act at a point. The magnitude of vector F_1 is 8.00 N, and its direction is an angle 64.0 degrees above the x-axis in the second quadrant. The magnitude of vecto
- Two forces, vector F_1 and vector F_2, act at a point. The magnitude of vector F_1 is 8.60 N, and its direction is an angle 57.0 degrees above the x-axis in the second quadrant. The magnitude of vecto
- Two forces, F1 of magnitude 60 Newtons (N) and F2 of magnitude 70 newtons, act on an object at angles of 40 and 130 respectively with the positive x axis. find the direction and magnitude of the resul
- Two forces, F_1 and F_2, act at a point. The magnitude of F_1 is 9.00 N, and its direction is an angle 65.0 degrees above the x-axis in the second quadrant. The magnitude of F_2 is 6.00 N, and its dir
- The force vector A has a magnitude of 97.0 newtons (N) and points due east. The force vector B has a magnitude of 107 N and points 71.4 degrees north of east. a. Find the magnitude and direction of A
- A force vector points at an angle of 54.9 degrees above the +x axis. It has a y component of +108 newtons (N). Find (a) the magnitude and (b) the x component of the force vector.
- Two forces each of magnitude 10 N have a resultant of magnitude 10 N. The angle between them is A) 90 degrees. B) 60 degrees. C) 120 degrees.
- A force vector points, at an angle of 51.6 degrees above the +x axis. It has a y component of +494 newtons (N). Find (a) the magnitude, and (b) the the x component of the force vector.
- Two forces, vector F_1 and vector F_2, act at a point. The magnitude of vector F_1 is 8.20 N, and is directed at an angle of 64.0 degrees above the negative x-axis in the second quadrant. The magnitud
- Two forces, vector F_1 and vector F_2, act at a point. Vector F_1 has a magnitude of 8.80 N and is directed at an angle of 60.0 degrees above the negative x-axis in the second quadrant. Vector F_2 has
- The force vector A has a magnitude of 70.0 newtons (N) and points due east. The force vector B has a magnitude of 111 N and points 71.4 north of east. Find the (a) magnitude and (b) direction of A -
- The force vector A has a magnitude of 79.0 newtons (N) and points due east. The force vector B has a magnitude of 107 N and points 75.0 north of east. Find the (a) magnitude and (b) direction of A -
- A force vector points at an angle of 51.6 degree above the +x axis. It has a y component of +494 newtons (N). Find (a) the magnitude and (b) the the x component of the force vector.
- A force vector points at an angle of 12.4 degrees above the +x axis. It has a y component of +337 newtons (N). Find the magnitude and the x component of the force vector.
- Two forces of magnitude 8 N making an angle of 30 degrees and 120 degrees with the +x-axis. Find the y component of the resultant.
- Find the magnitude and direction of the resultant force of two perpendicular forces F1=3 \ N and F2=4 \ N.
- Use the triangle forces method to determine the magnitude and direction of the resultant of the forces 13 N at 0 degrees and 25 N at 30 degrees.
- If the magnitude of the resultant force (of three forces shown) is 550 N and its direction measured clockwise from the positive x axis is 20 ^o, determine the magnitude of F_1 and the angle .
- Find the magnitude of the resultant of a 40 N force and a 70 N force acting concurrently when the angle between them is: a) 0.0 deg b) 30.0 deg c) 60.0 deg d) 90.0 deg e) 180.0 deg
- Consider P = 370 N and Q = 470 N. Determine the magnitude and direction of the resultant of the two forces.(a) The magnitude of the resultant of the two forces is (b) The direction of the resultant of
- Two forces act concurrently on point P. One force is 85 N in a direction 35 degrees north of east. The second 95 N force acts at an angle of 227 degrees. What is the magnitude and direction of the res
- A force of 75 \ N due north and 105 \ N due east is acting on a point. a. What is the magnitude and direction of the resultant force? b. What is the magnitude and direction of the equilibrant?
- Suppose two forces, one of a magnitude of 155 N at 65 degrees clockwise from the +x axis and one of a magnitude of 295 N in the +y direction acts on an object. Find the magnitude and direction of a third force that would be necessary for the object not to
- Two forces, \vec F_1 and \vec F_2 , act at a point. The magnitude of \vec F_1 is 9.80 N, and its direction is an angle 59.0 degrees above the x-axis in the second quadrant. The magnitude of \ve
- Two forces of magnitude 8 N making an angle of 30^\circ and 120^\circ with the x-axis. Find the y-component of the resultant force. A. 0 B. 4 N C. 8 N D. 16 N
- A force vector points at an angle of 50.8 degrees above the +x axis. It has a y component of +282 newtons. Calculate the magnitude of the force vector.
- Two forces 5 N and 10 N are acting at an angle of 120degrees between them. Find the resultant force in magnitude and direction.
- The bracket is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force F_R. a) Find the magnitude of the resultant force. b) Find coordinate direction angle \alpha of the resultant force. c)
- Determine the magnitude and direction of the resultant of the forces shown.
- A force vector \vec{F_1} points due east and has a magnitude of 150 newtons. A second force \vec{F_2} is added to \vec{F_1} . The resultant of the two vectors have a magnitude of 480 newtons a
- The angle between two forces of 32 N and 47 N is 36 degrees. Find the magnitude of the resultant force.
- Find the resultant, in magnitude and direction of a force of 40 N which makes an angle with the +x-axis of 38 degrees and a force of 20 N acting along the +x-axis. Find the x and y components of the r
- Consider three force vectors \vec{F}_1, \vec{F}_2 and \vec{F}_3 with magnitude 43 N and direction 53^\circ, magnitude 94 N and direction 162^\circ and magnitude 59 N and direction 288^\circ, respectively. All direction angles are measured counterclockwise
- Determine the magnitude and direction of the resultant force \vec{F}_R = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 of the three forces for the two cases shown below. First find the resultant \vec{F}^{'} = \ve
- Four displacement vectors, \vec{A}, \vec{B}, \vec{C}, and \vec{D}, are shown in the diagram below. Their magnitudes are: \vec{A} = 15.4 m, \vec{B} = 11.0 m, \vec{C} = 12.0 m, and \vec{D} = 26.0 m. What is the magnitude and direction of the resultant vecto
- The resultant of two forces acting at an angle of 60^o is \sqrt {61} if they act at a right angle. Their resultant is \sqrt {41}, find the magnitude of the force.
- Find the magnitude of two forces such that, if they act at a right angle, their resultant is \sqrt{10}\ N and when they act at an angle 60º their resultant is \sqrt{13}\ N.
- A force has an x-component of 3 N and a y-component of -5 N. Draw this vector. What angle does this force make with the positive x-axis? What is the magnitude of the force?
- The magnitudes of the four displacement vectors shown in the drawing are A = 14.0 m, B = 10.0 m, C = 13.0 m, and D = 29.0 m. Determine the magnitude and direction of the resultant that occurs when these vectors are added together.
- Two forces whose resultant is 10 N, are perpendicular to each other. If one of them makes an angle of 60 degrees with the resultant, calculate its magnitude.
- The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 \ m, B = 10.0 \ m, C = 11.0 \ m, and D = 23.0 \ m. Determine the: a) magnitude and b) direction for the resultant that occurs when these vectors are added together. Speci
- The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 12.0 m, C = 13.0 m, and D = 25.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the dir
- A 80 N and a 60 N force act concurrently on a point. Find magnitude of the vector sum if the forces pull in: a. the same direction, b. the opposite direct and c. at right angles to each other.
- Draw the FBD. Determine the magnitude of the resultant force and its direction, measured clockwise from the positive y-axis.
- Two forces act on a point object as follows: 100 N at 170.0 degrees and 100 N at 50.0 degrees. Find their resultant.
- Given four vectors: 16 newtons at 20 degrees north of west, 25 newtons due south, 10 newtons due east, and 30 newtons at 55 degrees south of west, find the resultant magnitude and the resultant angle based on the zero-degree x-axis.
- Calculate the magnitude and directional cosines of the resultant force \vec{F}_R, for three forces shown in the figure below. Given, \vec{F}_1 = -5 \hat{i} + 3 \hat{j} + 1.5 \hat{k}, \vec{F}_2 = 3 \ha
- Three forces act on the bracket. Determine the magnitude and direction theta of F so that the resultant force is directed along, the positive x-axis and has a magnitude of 8 kN.
- The magnitudes of the four displacement vectors shown in the drawing are A = 16.3 m, B = 10 m, C = 12.9 m, and D = 26.9 m. Determine the magnitude of the resultant vector that occurs when these vectors are added together.
- Two forces whose magnitude are in a ratio of 3:5 give a resultant of 35 N if the angle of inclination is 60 degrees. Calculate the magnitude of each force.
- Vector A = 6.0 m and points 30 degrees north of east. Vector B = 4.0 m and points 30 degrees west of north. Find the magnitude and direction of the resultant vector.
- Forces of 70 N at 140 degrees, and 30 N at an angle of 280 degrees, measured counter-clockwise from the positive x-axis, act on an object. What is the magnitude of the resultant force (in Newtons)? Wh
- Forces of 70 N at 40 degrees, and 10 N at an angle of 260 degrees, measured counter-clockwise from the positive x-axis, act on an object. What is the magnitude of the resultant force (in Newtons)? Wha
- Forces of 60 N at 130 degrees, and 10 N at an angle of 310 degrees, measured counter-clockwise from the positive x-axis, act on an object. What is the magnitude of the resultant force (in Newtons)? Wh
- Forces of 70 N at 160 degrees, and 10 N at an angle of 180 degrees, measured counter-clockwise from the positive x-axis, act on an object. What is the magnitude of the resultant force (in Newtons)? Wh
- The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 10.0 m, C = 14.0 m, and D = 25.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the dir
- Two forces F 1 and F 2 act on a particle. F1 has magnitude 8 N and in direction 90 degrees. Find the magnitude and direction of their resultant.
- A force of 8 N at 15 degrees from the x-axis is added with a force of 12 N 220 degrees from the x-axis. What is the magnitude and angle from the x-axis of the resultant vector?
- In the drawing, what is the vector sum of forces \vec{D} + \vec{E} + \vec{F} if each grid square is 2.0 N on a side. A) magnitude and B) angle.
- Two forces whose resultant is 98 \ N are perpendicular to each other. If one of them makes an angle of 63.7^o with the resultant, calculate its magnitude.
- The resultant \vec{R} of the two forces \vec{F}_u, \vec{F}_v has magnitude 600 lb, and the angle between the line of action of the resultant and y axis is 28^\circ. Determine the magnitude of the forc
- Two forces act concurrently on a point P. One force is 60nt due east. The second force is 80nt due north. (a) Find the magnitude and direction of their resultant. (b) What is the magnitude and directi
- Two forces whose resultant is 100 newtons are perpendicular to each other. If one of them makes an angle of 60 degrees with the resultant, calculate its magnitude.
- A force vector \vec{F}_1 points due east and has a magnitude of 105 newtons. A second force \vec{F}_2 is added to \vec{F}_1. The resultant of the two vectors has a magnitude of 895 newtons and points
- Consider three force vectors \vec{F}_1 with magnitude 42 N and direction 140^\circ, \vec{F}_2 with magnitude 27 N and direction -110^\circ, and \vec{F}_3 with magnitude 19 N and direction 120^\circ. All direction angles are measured counter-clockwise from
- Find the resultant vector of a force of 80 N acting at 47° counterclockwise from the y axis and a force of 68 N acting at 52° clockwise from the y axis,
- The magnitudes of the two vectors shown in the diagram below are: |\vec{A}| = 132 and |\vec{B}| = 145. Find the magnitude and direction (counterclockwise angle made with the +x axis) of the vector: \v
- Two forces, F 1 and F 2, act at a point. The magnitude of F 1 is 9.80 N , and its direction is an angle 59.0 degree above the x-axis in the second quadrant. The magnitude of F 2 is 6.40 N , and its di
- Two forces 10\ \mathrm{N} acting in the direction N\ 30^{\circ} east and 15\ \mathrm{N} acting in the eastern direction. If both forces act at a point, find the magnitude and direction of (a) the resultant force (b) the equilibrant force.
- Two forces who's resultant is 10N,are perpendicular to each other if one of them make an angle 60 degree with their resultant. Calculate its magnitude.
- the sum of the magnitude of two forces acting at a point is 18 and the magnitude of their resultant is 12.if the resultant is at 90 degree with the force of the smaller magnitude, then their magnitude
- The following force vectors act on an object: i) 50 Newtons at 45 degrees north of east and ii) 25 Newtons at 30 degrees south of east. Which of the following represents the magnitude of the resultant force and its angle relative to the easterly direction
- Determine F_1, as a Cartesian vector, so that the resultant force applied to the ring A is pointing upward (vertically) and has a magnitude of 800 N. What is the magnitude and direction of F_1?
- Determine the resultant (magnitude, direction, and line of action) of the two forces acting on the block shown below. Force \vec{F_{1 has a magnitude of 180 N and force \vec{F_{2 has a magnitude of 100 N.
- Two forces acts on a point. 100N at 170 degrees from the +x-axis and 150N at 50 degrees. Find their resultant force and the direction, from the +x-axis.
- Determine the magnitude and direction theta of the resultant force F_R . Express the result in terms of the magnitudes of the components F_1 and F_2 and the angle phi
- Given the vector F = 18 N, theta = 83 degrees, find the magnitude and direction of the opposite vector F.
- Vector A has a magnitude of 12.6, m and a direction of -84.0 degrees. Vector B has a magnitude of 34.0, m and a direction of -75.0 degrees. What is the resultant magnitude and direction of a vector that is equal to A + B ? a. Magnitude 20.6
- Three forces F_1, F_2 and F_3 act on an object as shown in the free-body diagram above. F_1 has a magnitude of 6 N while F_2 and F_3 each have a magnitude of 3 N. All forces make angles of 30^\circ� w
- A vector has magnitude V(1) = 46 N, and direction theta(1) = 30 degrees. Another vector V(2) = 63 N, and direction theta(2) = 151 degrees. Calculate the reference angle of the vector V(1) + V(2). Roun
- A 150-N and 80-N force act upon an object. The angle between the two forces is 55 degrees. Determine the magnitude and direction by trigonometric calculations.
- If \theta = 60^{\circ} and F = 450 N, Determine the magnitude of the resultant force and its direction ( measure clockwise direction from x-axis).
- Force A points at 30 degrees above the horizontal direction and has a magnitude of 100 N. Force B points at 53.1 degrees below the horizontal direction and has a magnitude of 200 N. Determine the magnitude and direction of the acceleration of an object o
- Vector A has a magnitude of 4.0 m and points 30 degrees south of east. Vector A has a magnitude of 2.0 m and points 30 degrees north of west. The resultant vector A + B is given by
- Consider two vectors F_1 with magnitude 44 N inclined at 163^{\circ} and F_2 with magnitude 72 N inclined at 236^{\circ}, measured from the positive x-axis with counterclockwise positive. A) What is the magnitude of the resultant vector F_1 + F_2? Draw th
- If the magnitude of the resultant force is to be 510 N, directed along the +y axis, determine, a. the magnitude of force F. b. the angle \theta. Express your answer to two significant figures.
- Two forces of 2 N and 3 N, respectively, make an angle of 50 degrees with each other. Find the resultant analytically by applying the cosine law, namely, R^2 = A^2 + 2 A B cos (theta) + B^2, where A and B are the two forces and R is the resultant.
- Two forces of 2 N and 3 N, respectively, make an angle of 90 degrees with each other. Find the resultant analytically by applying the cosine law, namely, R^2 = A^2 + 2 A B cos (theta) + B^2, where A and B are the two forces and R is the resultant.
- Three forces act on the bracket. Determine the magnitude and direction of F1 so that the resultant force is directed along the positive x' axis (60 degrees from F2) and has a magnitude of 800 N.
- What is the resultant magnitude and direction these two forces?
- The forces of magnitude 60 newtons(N) and 10 Newtons act on an object at angle of 30 and - 45 with the positive x-axis. Find the direction and magnitude of the late resultant force,that is find F1 +
- Two forces: F_1: 200g, 0^o \\F_2: 150g, 120^o, find the resultant vector.
- A force vector has a magnitude of 576 newtons and points at an angle 43 of below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector?
- The sum of magnitudes of two forces acting at a point is 18N and the magnitude of their resultant is 12N. If the resultant makes an angle of 90 degree with the force of smaller magnitude, what are the
- Two vectors of magnitudes 25 N and 22 N act at right angles to each other. What is the magnitude of their resultant? Answer in units of N
- Two forces, F_1 and F_2, act at a point. F_1 has a magnitude of 8.80\ \mathrm{N} and is directed at an angle of 64.0 degree above the negative x axis in the second quadrant. F_2 has a magnitude of 7.00\ \mathrm{N} and is directed at an angle of 52.8 degre
- Determine the magnitude of the resultant force and its direction (measured counterclockwise from the +x axis) for the figure below.
- What is the magnitude and direction of the resultant of these two forces?
- Two forces whose resultant is 100N are perpendicular to each other. If one of them makes an angle of 60 with the resultant, calculate its magnitude.
- F-250 N Express the two forces in Cartesian vector form. Determine the magnitude and coordinate direction angles of the resultant. Force F1 is rotated 25 degrees from the y axis in the x-y plane and 35 degrees down in the z-direction.
Explore our homework questions and answers library
Browse
by subject