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# Scalar and Vector Operations

### Kinematics and Energy Kinematics

Could you provide workings out and answers to the following physics questions: 1.a. What is the difference between a scalar and a vector quantity? b. A hiker walks due north for 4.0 km to reach point A and then northeast for 6.0 km to reach point B. Find by calculation or by scale drawing: - the straight line distance from s

### Keeping a derrick from tipping

A load having a mass of 9.2 metric tons is to be lifted by means of a contractor's derrick as shown in fig 5-10. If the Vertical plane containing the boom bisects the angle ADB, what reactions must be provided at points A and B to keep the derrick from tipping? The boom has a mass of 1.84 metric tons, and it makes an angle of 4

### Physical principles; difference between a vector and scalar distance, difference between speed and velocity

1. Understanding physical principles is often very useful in everyday life. For example, a skater develops an intuitive understanding of angular momentum in order to master making turns, and virtually all of us as car drivers come to understand the principles of inertia, velocity, and linear momentum. Can you name at least

### Calculations for Vectors

Please provide formulas and step by step instructions on how to solve. A Vector F has a magnitude of 20 and is directed vertically downward. Find is components Fx and Fy in each of the coordinate frames. Please see attached.

### Solving Vector Problems

Hi, I am having a lot of difficulty understanding vectors, can you please assist me with these questions. Given: position vector A = i hat. position vector B = i hat + j hat + k hat. 1) Find A hat and B hat (unit vector in that direction). 2) Find position vector C in that plane perpendicular to position ve

### Area; Scalar; Vector; Cross Product etc...

Please assist me with the attached problems, including: 1. Find the area within the given set of points 2. Determine whether each product is a scalar or a vector or does not exist. Explain reasoning. See attachment for complete list of problems. Thanks

### MAGNITUDE OF A VECTOR

If A=(12i-16j) and B=(-24i+10j),what is the magnitude of vector C=(2A-B)?

### Solving for Vector Addition and Subtraction

Question: Two vectors act upon a body at an angle of 45 degrees between them. Vector A has a magnitude of 100.0 and vector B has a magnitude of 200.0. Draw an XY coordinate system. What are the x and y components of the resultant vector? What is the magnitude of the resultant, and it's directions angle with respect to the A vec

Draw a scaled diagram of a vector of magnitude 100cm at 30 degrees above the horizontal and use trigonometry to determine its x and y components.

### Determining the sum of vectors

Please see attached file for the diagram. Three vectors are shown in Fig. 3-41 (A = 66.0, O = 52.0 degrees). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. Rx = ? Ry = ? (b) What is the magnitude of the resultant? What is the res

### Extremal paths.

Consider the action for a particle in a potential U. a. Show that an extremal path is never that of a local maximum for the action. ("Local" means relative to nearby paths). b. Find an example in which an extremal path is that of a local minimum for the action. c. Find an example in which an extremal path is not that of a

### Vectors Magnitudes and Angles

1) Both vectors A and B have a magnitude 5 and the angle between them is 53.13 degrees. Calculate the magnitude of A+B. 2) The diagram shows vector C. Determine the X and Y components of C. see attached file for details

What is the resultant displacement if we follow these directions? 75.0 m N 95.0 m at 18.0 degrees N of E 65.0 m at 34.0 Degrees W of N 25.0 m SW 20.0 m E

### Evaluating quantities of vectors

Two vectors are given by A = -3i + 7j -4k and B = 6i -10j + 9k. Evaluate the quantities: a) cos^-1 [A.B/AB] ( the . between the A.B is a dot product) b) sin^-1 [ |A x B|/AB] c) Which gives the angle between the vectors. I haven't a clue as to what to do with this problem. Do I use the cross products of unit vectors t

### Vector Dot Product Calculations

Vector Dot Product Let vectors , , and . Calculate the following: A. = Answer not displayed C. = Answer not displayed E. = Answer not displayed G. = Answer not displayed H. Express your answer numerically in radians, to three significant figures. Angle between and = Answer not displaye

### Find the Vector Sum

Three vectors have the same magnitude of 14 units. They make angles of t, 2t, and 3t with respect to the x axis, where t = 20 degrees. What is their vector sum?

### Vector Problems Solved

On the problem, or any problem how do you know which x or y vector to draw first and which or where to get your angles. Where put theta? Please explain and help any way you can simple enough for me to understand.

### Vector Additions - Analytically and Graphically

See the attached file. Finding the vector sum of three forces 1) Experimental method: Use F1 of 160g at 280 degrees, F2 of 105 grams at 60 degrees and F3 of 75g at 15 degrees counter clockwise from the +y axis. Determine the equilibriant and the resultant of the three vectors experimentally. Record magnitude and direction

### Vectors and magnitude

Please give the solution and step by step instructions on how to do these. I learn by examples. 1) Vector A has a magnitude of 10. Vector B has a magnitude of 7. The magnitude of the vector sum of A and B is 17 3 -3 between 17 and -3 none of these 2) To find magnitude of a vector calc the sum of its components

### Calculating magnitude of a vector and height

If A = (12i - 16j) and B = (-24i+10j), what is the magnitude of the vector C=(2A-B)? Answers: a) 42 b) 22 c) 64 d) 90 An archer shoots an arrow with a velocity of 45 m/s at an angle of 50 degrees with the horizontal. What is the height of the arrow at a point 150 meters downrange? Answers: a) 4.7 m b) 47.0 m c) 5

### Calculating Displacement in a Yacht Race

Question: In a yacht race the boats sail around three buoys. What is the displacement from the last buoy to the starting point? (a) unit vector notation (b) magnitude and direction? From the origin to Buoy #1 is R1, From Buoy #1 to Buoy #2 is R2, (30 degrees clockwise from R1) From Buoy #2 to Buoy #3 is R3. (120 degree

### Angle between two vectors

The vector A has a magnitude of 6m and vector B has magnitude of 4 m. That is the angle between them if the magnitude of the resultant is (a) 3m (b) 8m? Let vector A lie along the x-axis. Do each part graphically and by components.

### Proving Vector Functions

Prove that S*(PxQ) = P*(QxS) where * is dot product and x is cross product if S=Sxi+Syj+Szk P=Pxi+Pyj+Pzk Q=Qxi+Qyj+Qzk

### Vector Components

In 1992, Akira Matsushima, from Japan, rode a unicycle across the United States, covering about 4800 km in six weeks. Suppose that, during that trip, he had to find his way through a city with plenty of one way streets. In the city center, Matsushima had to travel in sequence 280 m north, 220 m east, 360 m north, 300 m west, 1

### Different Vector Notation Magnitudes and Direction

A) Vector E has a magnitude of 17.0 cm and is directed 27.0 degrees counterclockwise from the +x axis. Express it in unit vector notation. b) Vector F has a magnitude of 17.0 cm and is directed 27.0 degrees counterclockwise from the +y axis. Express it in unit vector notation. c) Vector G has a magnitude of 17.0 cm and is dire

### Vector Analysis - Spiderweb

A spider is resting after starting to spin its web. The gravitational force on the spider is 0.150 Newton down. The spider is supported by different tension forces in the two strands above it, so that the resultant vector force on the spider is zero. The two strands are perpendicular to each other, so the x and y directions h

### Electric force on an electron

What is the electric force (with direction) on an electron in a uniform electric field of strength 2780 N/C that points due east? Take the positive direction to be east.

### Mass and cord tension of mass on a frictionless plane

A block with unknown mass M is held stationary on a frictionless plane inclined at angle b= 30 degrees, by a cord attached to the ceiling. The angle between cord and ceiling is angle a=50 degrees. The normal force exerted on the block by the plane is N= 74 nt. SEE ATTACHMENT #1 for arrangement. Part a. On the diaqram shown as

### A hunter aims directly at a target; by how much will he miss

A hunter aims directly at a target (on the same level) 103 m away. If the bullet leaves the gun at a speed of 255 m/s, by how much will it miss the target? I'm assuming that the bullet will miss the target because it arcs down toward the ground as it moves horizontally. But don't I need to know how far off the ground it is in

### Subtracting Vectors Lengths

"The figure below (please see attached Word file) shows three vectors of lengths A = 67.8, B = 39.5, and C = 47.0. The angles are theta(a) = 28.8° and theta(b) = 54.5°, and C points along the negative y-axis. Determine the length of the vector A - C." The book indicates that the equation for subtraction of vectors is si