Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

3. Vectors

Adding Vectors by Components

Physics

3. Vectors

Adding Vectors by Components

Previous problemNext problem

4:06 minutes

Problem 32

Textbook Question

A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

Verified step by step guidance

Identify the vectors involved in the problem. The postal employee's route consists of three segments: 2.6 km north, 4.0 km east, and 3.1 km at a 45-degree angle north of east.

Break down each vector into its components. For the first vector (2.6 km north), the components are: x-component = 0 km, y-component = 2.6 km. For the second vector (4.0 km east), the components are: x-component = 4.0 km, y-component = 0 km.

For the third vector (3.1 km at 45 degrees north of east), use trigonometry to find the components: x-component = 3.1 km * cos(45°), y-component = 3.1 km * sin(45°).

Add the components of all vectors to find the resultant vector. Sum the x-components: 0 km + 4.0 km + (3.1 km * cos(45°)). Sum the y-components: 2.6 km + 0 km + (3.1 km * sin(45°)).

Calculate the magnitude of the resultant displacement using the Pythagorean theorem: magnitude = sqrt((sum of x-components)^2 + (sum of y-components)^2). Determine the direction using the arctangent function: direction = arctan((sum of y-components) / (sum of x-components)).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Addition

Vector addition involves combining two or more vectors to determine a resultant vector. This process can be visualized graphically by placing the tail of one vector at the head of another, forming a triangle or polygon. The resultant vector is drawn from the tail of the first vector to the head of the last vector, representing the overall effect of the individual vectors.

Components of a Vector

Vectors can be broken down into their components along the axes of a coordinate system, typically the x and y axes. This method simplifies calculations, as each component can be treated as a separate scalar quantity. The magnitude of the resultant vector can be found using the Pythagorean theorem, while the direction can be determined using trigonometric functions such as sine and cosine.

Resultant Displacement

Resultant displacement is the overall change in position from the starting point to the endpoint, represented as a single vector. It accounts for both the distance traveled and the direction of travel. In this context, calculating the resultant displacement involves summing the individual displacements along the route and determining the final position relative to the starting point.

Watch next

Master Vector Addition By Components with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

FIGURE P3.46 shows four electric charges located at the corners of a rectangle. Like charges, you will recall, repel each other while opposite charges attract. Charge B exerts a repulsive force (directly away from B) on charge A of 3.0 N. Charge C exerts an attractive force (directly toward C) on charge A of 6.0 N. Finally, charge D exerts an attractive force of 2.0 N on charge A. Assuming that forces are vectors, what are the magnitude and direction of the net force F_netexerted on charge A?

499

views

Textbook Question

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. From 8:00 to 9:00 a.m.

\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}

\overset{⇀}{B} = - 7.0 \hat{i}

, and

\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}

. What is the direction of

\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}

? Express your answer in degrees counter clockwise from the positive x axis.

\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}

\overset{⇀}{B} = - 7.0 \hat{i}

, and

\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}

. What is the magnitude of

\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}

739

views

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference B - A

1784

views

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference A - B

2735

views

Textbook Question

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector sum A + B

2054

views

Textbook Question

FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving? Give the direction as an angle below the negative x-axis.

1794

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap