Chapter 4: Q2Q (page 82)

Figure 4-22 shows the initial position i and the final position f of a particle. What are the (a) initial position vector $\vec{r_{1}}$ and (b) final position vector $\vec{r_{f}}$ , both in unit-vector notation? (c) What is the x component of displacement $∆ \vec{r}$ ?

Short Answer

Expert verified

a) Initial position vector $\vec{r_{i}} = 7 \overset{⏜}{i} + \overset{⏜}{j} - 2 \overset{⏜}{k}$

b) Final position vector $\vec{r_{f}} = 5 \overset{⏜}{i} - 3 \overset{⏜}{j} + \overset{⏜}{k}$

c) The x component of displacement $∆ \vec{r} = - 2 \overset{⏜}{i}$

Step by step solution

Given information

$r_{i x} = 7 m r_{i y} = 1 m r_{i z} = - 2 m r_{f x} = 5 m r_{f y} = - 3 m r_{f z} = 1 m$

To understand the concept

Vector can be written by measuring the distances along each direction. Displacement can be calculated by change in position between two vectors.

Formulae:

Unit vector notation

$\vec{r} = r_{x} \overset{⏜}{i} + r_{y} \overset{⏜}{j} + r_{z} \overset{⏜}{k}$

(a) To find initial position vector r1→

Initial position vector $(\vec{r_{1}})$

$\vec{r_{1}} = r_{i x} \overset{⏜}{i} + r_{i y} \overset{⏜}{j} + r_{i z} \overset{⏜}{k} \vec{r_{1}} = 7 \overset{⏜}{i} + \overset{⏜}{j} - 2 \overset{⏜}{k}$

(b) To find initial position vector rf→

$\vec{r_{f}} = r_{f x} \overset{⏜}{i} + r_{f y} \overset{⏜}{j} + r_{f z} \overset{⏜}{k} \vec{r_{f}} = 5 \overset{⏜}{i} - 3 \overset{⏜}{j} + \overset{⏜}{k}$

(c) To find x component of displacement ∆r→

We have, displacement vector is given by:

$∆ \vec{r} = \vec{r_{f}} - \vec{r_{i}} = (5 - 7) \overset{⏜}{i} + (- 3 - 1) \overset{⏜}{j} + (1 - (- 2)) \overset{⏜}{k} = - 2 \overset{⏜}{i} - 4 \overset{⏜}{j} + 3 \overset{⏜}{k}$

Hence,

The x component of the displacement is $∆ \vec{r} = - 2 \overset{⏜}{i}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Figure 4-22 shows the initial position i and the final position f of a particle. What are the (a) initial position vector $\vec{r_{1}}$ and (b) final position vector $\vec{r_{f}}$ , both in unit-vector notation? (c) What is the x component of displacement $∆ \vec{r}$ ?

Short Answer

Step by step solution

Given information

To understand the concept

(a) To find initial position vector r1→

(b) To find initial position vector rf→

(c) To find x component of displacement ∆r→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Torque and Rotational Motion

Translational Dynamics

Radiation

Famous Physicists

Astrophysics

Study anywhere. Anytime. Across all devices.

Figure 4-22 shows the initial position i and the final position f of a particle. What are the (a) initial position vectorr1→and (b) final position vectorrf→, both in unit-vector notation? (c) What is the x component of displacement∆r→?

Short Answer

Step by step solution

Given information

To understand the concept

(a) To find initial position vector r1→

(b) To find initial position vector rf→

(c) To find x component of displacement ∆r→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Torque and Rotational Motion

Translational Dynamics

Radiation

Famous Physicists

Astrophysics

Study anywhere. Anytime. Across all devices.

Figure 4-22 shows the initial position i and the final position f of a particle. What are the (a) initial position vector $\vec{r_{1}}$ and (b) final position vector $\vec{r_{f}}$ , both in unit-vector notation? (c) What is the x component of displacement $∆ \vec{r}$ ?