Fisica

Unidad I: Vectores

General Instructions: Any graphs should be done on squared paper, with the help of ruler and protractor.

I. Polar and Rectangular Forms of a Vector

Basis:
A vector is basically a quantity that possesses magnitude and direction. It can be given in the form of a set of numbers. The relationship between these numbers determines whether the vector is in polar orrectangular form.
If the vector is given as a real number giving its length and an angle to give its position, we say the vector is in polar form.
If the vector is given as a pair of real numbers in a specific order, such as an ordered pair, we say the vector is in rectangular form. Each of the two ordered numbers is one of the components of the vector and represents the vectors dimensions along thex- and y-directions.
When converting from polar to rectangular form we calculate the components using the sine and cosine ratios:
vx=v∙cosθ vy=v∙sinθ
When converting from rectangular to polar form we simply use the Pythagorean theorem and the tangent ratio:
v2=vx2+vy2 tanθ=vyvx
Two vectors are considered basically the same if they have the same magnitude and direction, regardless of wherethey are drawn on the plane.
When a vector is used to describe a physical quantity, the units are usually given after the magnitude (if in polar form) or at the end of the ordered pair (if in rectangular form). For example, a velocity vector could be v=5.0ms, ∠53.13° or v=3,4ms.

A. Draw the given vectors at the given starting point—vectors are written in rectangular form.
1. v1=7,-3starting at -2,-4
2. v2=-4,2 starting at 3,-1
3. v3=4,8 starting at -2,-6
4. v4=-2,-2 starting at 8,2
5. v5=-4,2 starting at 0,2

Among the above, are there vectors that are the same? Why? If so, which ones?
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1.
2.
3.
4.
5.

For problems 6-8, choose an appropriate scale todraw.
6. A velocity v=40.0,-33.0ms _________________
7. A displacement ∆d=-115,400 km _________________
8. An acceleration a=1.2,2.3ms2 _________________

To the right, write the approximate direction of the vectors, as in a map (SW, NE, etc.)

B. Draw the given vectors at the given starting point—vectors are written in polar form.
1. v6=8, ∠30° starting at 0,0
2.v7=2.8, ∠225° starting at -3,4
3. v8=6, ∠60° starting at 1,1
4. v9=8, ∠-330° starting at -2,-3
5. v10=5, ∠135° starting at 4,-1
Among the above, are there vectors that are the same? Why? If so, which ones?
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Are there any vectors in the first set (v1 to v5) that are equal to any in the second set (v6to v10)? If so, which ones?
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C. Convert each of the vectors in part A to polar form.

D. Convert each of the vectors in part B to rectangular form.

II. Multiplication of a Vector Times a Scalar

Basis:
When you multiply a scalar times a vector (a∙v), the result is a vector with the followingcharacteristics:
a. If a is a positive scalar, the magnitude of the resultant is the product of a and v, and the direction is the same direction v had.
b. If a is a negative scalar, the magnitude of the resultant is the product of –a and v (so the magnitude ends up being positive), and the direction is the opposite as that of v.
c. Finally, if the vector was given originally inrectangular form, the product may simply be calculated by multiplying each component times the scalar a: a∙x,y=ax,ay.

A. Given the following vectors, perform the given operations graphically following the steps below:
a. Graph the given vectors using an appropriate scale.
b. Draw the vector resulting from the multiplication on the same coordinate axis, starting from the same point....