Chapter 1 Units, Physical Quantities, and Vectors

55) The components of vector are B_x = -3.5 and B_y = -9.7, and the components of vector are C_x = -6 and C_y = +8.1. What is the angle (less than 180 degrees) between vectors and?

A) 124°

B) 56°

C) 17°

D) 163°

E) 106°

56) An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point.

A) 79 km

B) 81 km

C) 82 km

D) 78 km

E) 76 km

57) In the figure, the magnitude of vector is 18.0 units, and the magnitude of vector is 12.0 units. What vector must be added to the vectors and so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

58) Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes F₁ =1.0 N, F₂ =8.0 N and F₃ =7.0 N, where N is the standard unit of force, what is the component of the net force_net =₁+₂+₃ parallel to the floor?

A) 2.5 N

B) 5.1 N

C) 6.0 N

D) 7.8 N

59) As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F₁ = 80.0 N, F₂= 60.0 N, andF₃ = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

A) 180 N at an angle 60.0° with respect to +x-axis.

B) 60.0 N at an angle 90.0° with respect to +x-axis.

C) 20.0 N at an angle 34.3° with respect to +x-axis.

D) 35.5 N at an angle 34.3° with respect to +x-axis.

E) 40.0 N at an angle 60.0° with respect to +x-axis.

60) A teacher sends her students on a treasure hunt. She gives the following instructions:

1. Walk 300 m north

2. Walk 400 m northwest

3. Walk 700 m east-southeast and the treasure is buried there.

As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?

A) 187 m in a direction 67.3° north of east

B) 481 m in a direction 40.9° north of east

C) 399 m in a direction 52.5° north of east

D) 284 m in a direction 28.2° west of north

E) The treasure position cannot be reached in one straight walk.