Q2Q Figure 4-22 shows the initial po... [FREE SOLUTION]

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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 $\overset{鈫�}{r_{1}}$ and (b) final position vector $\overset{鈫�}{r_{f}}$ , both in unit-vector notation? (c) What is the x component of displacement $鈭� \overset{鈫�}{r}$ ?

Short Answer

Expert verified

a) Initial position vector $\overset{鈫�}{r_{i}} = 7 \overset{铃�}{i} + \overset{铃�}{j} - 2 \overset{铃�}{k}$

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

c) The x component of displacement $鈭� \overset{鈫�}{r} = - 2 \overset{铃�}{i}$

Step by step solution

Given information

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

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

$\overset{鈫�}{r} = r_{x} \overset{铃�}{i} + r_{y} \overset{铃�}{j} + r_{z} \overset{铃�}{k}$

(a) To find initial position vector r1→

Initial position vector $(\overset{鈫�}{r_{1}})$

$\overset{鈫�}{r_{1}} = r_{i x} \overset{铃�}{i} + r_{i y} \overset{铃�}{j} + r_{i z} \overset{铃�}{k} \overset{鈫�}{r_{1}} = 7 \overset{铃�}{i} + \overset{铃�}{j} - 2 \overset{铃�}{k}$

(b) To find initial position vector rf→

$\overset{鈫�}{r_{f}} = r_{f x} \overset{铃�}{i} + r_{f y} \overset{铃�}{j} + r_{f z} \overset{铃�}{k} \overset{鈫�}{r_{f}} = 5 \overset{铃�}{i} - 3 \overset{铃�}{j} + \overset{铃�}{k}$

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

We have, displacement vector is given by:

$鈭� \overset{鈫�}{r} = \overset{鈫�}{r_{f}} - \overset{鈫�}{r_{i}} = (5 - 7) \overset{铃�}{i} + (- 3 - 1) \overset{铃�}{j} + (1 - (- 2)) \overset{铃�}{k} = - 2 \overset{铃�}{i} - 4 \overset{铃�}{j} + 3 \overset{铃�}{k}$

Hence,

The x component of the displacement is $鈭� \overset{鈫�}{r} = - 2 \overset{铃�}{i}$ .

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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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91影视

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

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

Electric Charge Field and Potential

Electricity and Magnetism

Space Physics

Oscillations

Translational Dynamics

Particle Model of Matter

Study anywhere. Anytime. Across all devices.