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, 120 m south, 60.0 m east, 40.0 m south,90.0 m west (road construction) and then 70. m north. At that point he stopped to rest. Meanwhile, a curious crow decided to fly the distance from his starting point to the rest location directly ("as the crow flies"). It took the crow 40.0 seconds to cover the distance. Assuming the velocity of the crow was constant, find its magnitude and direction.

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Step 1. List given vectors. assume East is 0 degrees, North is 90 degrees, West is 180 degrees, and South is 270 degrees.
A= 280 m at 90 degrees, North
B= 220 m at 0 degrees, East
C= 360 m at 90 degrees, North
D= 300 m at 180 degrees, West
E= 120 m at 270 degrees, South
F= 60 m at 0 degrees, ...

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The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + ve

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.

See the attached file.
Could you please provide the answers and workings out to the following physics problems.
8. which one of the following quantities is a vector quantity?
a) the age of the earth
b) the mass of a football
c) the earth's pull on your body
d) the temperature of an iron bar
e) the number of people atte

PROBLEM 4. Let A_i(x) denote the components of a rank (0, 1) tensor field on a smooth n-dimensional manifold M , and let x = (x^1 , · · · , x^n ) denote a coordinate chart on an open subset U of M.
(a) Do the partial derivatives w_ij of A_j with resoect to x^i transform as a (0, 2) tensor under an arbitrary change of coord

1. Vector A = 119 grams @ 164°. What is Ax ?
2. Vector A = 119 grams @ 164°.What is Ay ?
3. Vector B = (114) xunit vector + (-32.8) yunit vector. Assume [grams] as the unit. What is the magnitude of B?
4. Vector B = (114) xunit vector + (-32.8) yunit vector. Assume [grams] as the unit. What is the direction of B in ra

PROBLEM 1. Let w = w_i dx^i be a 1- form (or covariant vector field) expressed in terms of the coordinate system x = (x^1, ... , x^n). Determine the (covariant) transformation law for the components w_i of w expressed in a new coordinate system y = (y^1, ... , y^n ). Describe the relationship between the contravariant and covari

How do I find the resultant of the three displacement vectors in the drawing by means of the component method? If the magnitudes of the vectors are A= 5 m B=5 m and C= 4 m?

(1) A force F of magnitude 6 in the direction i - 2j + 2k acts at the point P = (1,-1, 2).
a. Find the vector moment M of F about the origin.
b. Find the components of M in the direction of the (positive) x - axis, y -axis and z -axis.
c. Find the component of M about an axis in the direction

(See attached file for full problem description with proper symbols)
The position of a 2.75 x 10^5 N training helicopter under test is given by
Vector r = (0.020 m/s3)t3î + (2.2m/s)tĵ - (0.060 m/s2)t2k
Find the net force on the helicopter at t =5.0 s.
Express the vector F in the form Fx, Fy , Fz , where th

Real Analysis
Divergence Theorem
Let V be a region in 3complying with the hypotheses of the divergence theorem,
and denote by S its boundary surface. Let also φ: