Mastering Physics: Quiz 3

The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is

0°

Vector A has a magnitude of 7.0 m and points 30° east of north. Vector B has a magnitude of 5.0 m and points 30° west of south. The resultant vector A +B is given by

2.0 m at an angle 60° north of east.

If a vector A has components Ax > 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range

270° to 360°

A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

28 km

Vector A has a magnitude of 6.0 m and points 30° north of east. Vector B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A +B is given by

3.2 m at an angle of 8.3° south of east.

The x component of vector A is 5.3 units, and its y component is -2.3 units. The angle that vector A makes with the +x-axis is closest to

340°

The figure shows four vectors, A , B , C , and D . Vectors A and B both have a magnitude of 7.0 cm, and vectors C and D both have a magnitude of 4.0 cm. Find the magnitude of the sum of these four vectors.

4.2 cm

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

42 m/s at 31∘ north of west

Vector M = 4.00 m points eastward and vector N = 3.00 m points southward. The resultant vector M + N is given by

5.00 m at an angle of 36.9° south of east

An airplane undergoes the following displacements, all at the same altitude: First, it flies 59.0 km in a direction 30.0° east of north. Next, it flies 58.0 km due south. Finally, it flies 100 km 30.0° north of west. Use components to determine how far the airplane ends up from its starting point.

71.5 km

The magnitude of A is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. The components of A are closest to:

A x = -3.1 m, A y = 4.6 m.

The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

False

Three forces, F 1, F 2, and F 3, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is

0 N.

Find the direction of the sum of these four vectors

along the +y-axis

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

be directly over the package.

If A +B =C and their magnitudes are given by A + B = C, then the vectors A and B are oriented

parallel to each other (in the same direction).

The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

13

If a vector A has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range

180° to 270°

Three vectors, S , T , and U have the components shown in the table. What is the magnitude of the resultant of these three vectors? x component y component S 3.50 m -4.50 m T 2.00 m 0.00 m U -5.50 m 2.50 m

2.00 m

When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity?

4.8 m/s

Vector A has a magnitude of 8.0 m and points east, vector B has a magnitude of 6.0 m and points north, and vector C has a magnitude of 5.0 m and points west. The resultant vector A + B +C is given by

6.7 m at an angle 63° north of east

If a vector A has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range

90° to 180°

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

between 7.0 m and 17.0 m

A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector? Choice Northward Compo Eastern Compo. 1 29.4 m 17.0 m 2 18.2 m 28.1 m 3 22.4 m 11.5 m 4 17.0 m 29.4 m 5 25.2 m 18.2 m

choice 4

Two perpendicular vectors, A and B , are added together giving vector C . If the magnitudes of both vectors A and B are doubled without changing their directions, the magnitude of vector C will

increase by a factor of 2.