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 $∆ \vec{r} = - 2 \overset{⏜}{i}$ .

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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.

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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

Famous Physicists

Thermodynamics

Classical Mechanics

Conservation of Energy and Momentum

Physical Quantities And Units

Engineering Physics

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 $∆ \vec{r}$ ?