Vectors 222

A jogger runs 5.0 km on a straight trail at an angle of 60° south of west. What is the southern component of the run rounded to the nearest tenth of a kilometer? -4.3 km -2.5 km 2.5 km 4.3 km

-4.3 km

A helicopter flies 250 km on a straight path in a direction 60° south of east. The east component of the helicopter's displacement is ⇒

125 km

Suppose two initial vectors intersect at a right angle and form a resultant vector. The magnitudes of one initial vector, A, and the resultant vector, R, are given. Which formula can be used to find the magnitude of the other initial vector, B? B2 = A2 - R2 B2 = R2 + A2 B2 = A + R B2 = R2 - A2

B2 = R2 - A2

Which equation represents the Pythagorean theorem, which can be used to find the magnitude of resultant vectors? R = A + B R = A x B R2 = A2 x B2 R2 = A2 + B2

R2 = A2 + B2

The diagram shows components that have been added together to form Rx and Ry. Rx and Ry are the components of the resultant vector. Which formula can be used to find the magnitude of the resultant vector? R2 = Rx2 + Ry2 R = Rx + Ry R = Rx(cosθ) R = Rx(sinθ)

R2 = Rx2 + Ry2

The components of a vector are the parts of the vectors that are to each other.

perpendicular

A resultant vector is the of two or more vectors.

sum

The diagram shows three different bicycle routes taken by Frank, Alexis, and Juan to get to the electronics store. According to the diagram, Juan traveled kilometers.

10

The diagram shows vectors that are not perpendicular to one another. The data table shows the magnitudes of the components of each displacement vector. What is the angle of the resultant vector, rounded to the nearest tenth? 0.1° 10.0° 36.9° 41.1°

36.9°

Two vectors, X and Y, form a right angle. Vector X is 48 inches long and vector Y is 14 inches long. The length of the resultant vector is inches.

50

Study the vector diagram. What is the magnitude of vector X? 54 cm 72 cm 5184 cm 5625 cm

72 cm

In order to use the Pythagorean theorem to find the magnitude of a resultant vector, which must be true regarding the two initial vectors? They form a 90 degree angle. They are equal in magnitude. They have the same directions. They are parallel to one another.

They form a 90 degree angle.

Study the vector diagram. Which formula can be used to find the x-component of the resultant vector? Tx - Ux - Vx Tx + Ux + Vx Tx = Tcosθ Tx = Tsinθ

Tx + Ux + Vx

Two vectors are shown. Which statement best compares the vectors? Vector X has greater magnitude than vector Y. Vector Y has greater magnitude than vector X. The vectors have the same displacement. The vectors have the same direction.

Vector Y has greater magnitude than vector X.

The diagram shows three vectors. Which best describes a relationship among the vectors? Vectors P and Py are components of vector Px. Vectors Px and Py are components of vector P.

Vectors Px and Py are components of vector P.

The diagram shows two sets of vectors that result in a single vector. What are the first two steps for finding the magnitude of the resultant vector? find the square of the first horizontal vector and the square root of the first vertical vector find the square root of the first horizontal vector and the square root of the second horizontal vector find the sum of the two horizontal vectors and the sum of the two vertical vectors find the difference between the two horizontal vectors and the difference between the two vertical vectors

find the sum of the two horizontal vectors and the sum of the two vertical vectors

The angle a vector makes with the x-axis of a coordinate system must be what size in order to make one or more of its components negative? less than 30 degrees between 30 and 60 degrees between 61 and 90 degrees greater than 90 degrees

greater than 90 degrees

The diagram shows components that have been added together to form Rx and Ry. Rx and Ry are the components of the resultant vector. Which formula can be used to find the angle of the resultant vector?

tantheta= Ry/Rx