PHYSICS SMARTBOOK VECTORS

perpendicular

Components are projections of a vector parallel to the x-axis and parallel to the y-axis. This means that the components of a vector are _______ to each other.

52.5 N

Find the magnitude of the sum of a 25.0 N force and a 34.0 N force, given that the angle between the two vectors when aligned tip to tail is 125°.

angle; positive

The direction of a vector is defined as the ____ that the vector makes to the _____ x-axis, rotated counterclockwise.

magnitude; direction

When vectors are to be added graphically in two dimensions, vectors can be moved around freely, as long as their ______ and _____ do not change

IV

A vector has been placed into its proper quadrant. If the x-axis component is positive, while the y-axis component is negative, in which quadrant is the vector located?

Ax = (45 N) cos 38°, Ay = (45 N) sin 38°

A vector of magnitude 45 N is at a counterclockwise angle of 38° to the positive x-axis. Which are the correct components of this vector?

230.4°

After combining components of two vectors to be added, it was found that the resultant vector has an x-component of -17.7 cm and a y-component of -21.4 cm. What angle measured counterclockwise from the positive x-axis will properly describe the direction of the resultant vector? (Round to the nearest tenth of a degree.)

two; added or combined

Writing vectors in components allows for more than ____ vectors to be ____ easily. The process is much more difficult, however, when the vectors must be added graphically.

83.9 km

You travel 58.3 km in the direction of 15.0° north of east, then travel 77.3 km directly south. What is the magnitude of your net displacement? (Round to three significant figures.)

the tangent ratio

After the magnitude of the resultant vector for the addition of two perpendicular vectors is found using the Pythagorean theorem, the direction still needs to be found. The angle between vector A and the resultant vector in the diagram requires which trigonometric ratio?

pythagorean

Because the components of vectors being added are perpendicular, use the _____ theorem to find the magnitude of recombined resultant components, then use the ____ ratio for its direction.

Ax = A cos θ and Ay = A sin θ

For vector A, rotated counterclockwise through an angle of θ to the positive x-axis, the components of this vector can be expressed as

components

Projections of a vector parallel to the x-axis and parallel to the y-axis are its ____

1) choose a coordinate system 2) resolve vectors into x- and y- components 3) add or subtract the components in the x- direction, then separately add or subtract the components in the y- direction 4) apply the Pythagorean theorem to find the magnitude of the resultant vector and the tangent ratio to find its direction

Put the following steps in order from first step to last step, when using components to add vectors algebraically.

vector resolution

The process of breaking a vector into its components is ____

cos; <s v="1"><p><t s="6">-</t><t>0.707</t></p></s> or <s v="1"><p><t s="6">-</t><t>.707</t></p></s> sin; <s v="1"><p><t s="6">-</t><t>0.707</t></p></s> or <s v="1"><p><t s="6">-</t><t>.707</t></p></s>

Vector A is at a 225° angle measured counterclockwise from the positive x-axis. When it is written in components, Ax = A____225° =____A, and Ay = A____225° =____A. (Round to three significant figures.)

24.9

Vector A points along the positive x-axis and has a magnitude of 22.0 km. Vector B points counterclockwise from the positive x-axis at an angle of 58° with a magnitude of 17.0 km. The magnitude of the resultant vector is found to be 34.2 km. The direction of the resultant vector will be _____ ° rotated counterclockwise from the positive x-axis. (Round to three significant figures.)

93 km north

What is the result of the addition of the vectors 125 km north and 32 km south?

The vectors must be at an angle other than 0° or 180° to each other.

What must be true of vectors in order for them to be two-dimensional?

The x- and y-components of vectors can be added as if each component direction were one-dimensional.

Which statement best describes why vectors are written in components?

the tail of the vector at the origin, with the positive x-axis pointing east and the positive y-axis pointing north.

When a vector is to be placed onto a coordinate system, the usual arrangement is to place

parallel

When a vector representation involves motion along an incline, it is often convenient to place the positive x-axis in the direction of motion that is ____ to the inclined surface.

- A protractor and ruler can be used to draw the vectors with the correct angles and magnitudes, so that the resultant vector can then be measured. - The resultant always points from the tail of the first vector to the tip of the final vector.

When adding vectors in two dimensions, which statements are correct?

perpendicular; resultant

When finding the sum of two _____ vectors, the Pythagorean theorem can be used to find the _____ magnitude

angle; cosines

When two vectors are added, and the magnitudes of the two vectors and the contained _____ between them are given, the magnitude of the resultant vector can be found using the law of ____

- the law of sines - the law of cosines

When two vectors that are at an angle other than 90° to each other are added, which mathematical techniques can be used to find the resultant vector?

- A = √(Ax)2+(Ay)2Ax2+Ay2 - A = Ax + Ay

When vector A is represented using vector components Ax and Ay, which vector equations are correct?

tip; first; tip

When vectors are added in one dimension, the vectors being added are arranged ____ to tail and the resultant vector points from the tail of the ___ vector to the _____ of the final vector

- Three people pull on ropes in slightly different directions to get a car out of some deep mud. - A boat moving west is moved by a current moving north. - You push a heavy object with a force directed to the west as it moves southward on an icy surface.

Which situations are examples of vectors in two dimensions?

- Three people pull on ropes in slightly different directions to get a car out of some deep mud. - You push a heavy object with a force directed to the west as it moves southward on an icy surface. - A boat moving west is moved by a current moving north.

Which situations are examples of vectors in two dimensions?