Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
9th Edition
ISBN: 9781305116429
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 1.73AP

You stand in a flat meadow and observe two cows (Fig. P1.73). Cow A is due north of you and 15.0 m from your position. Clow B is 25.0111 from your position. From your point of view, the angle between cow A and cow H is 20.0°, with cow B appearing to the right of cow A. (a) How far apart are cow A and cow B? (b) Consider the view seen by cow A. According to this cow, what is the angle between you and cow B? (c) Consider the view seen by cow B. According to this cow, what is the angle between you and cow A? Hint: What does the situation look like to a hummingbird hovering above the meadow? (d) Two stars in the sky appear to be 20.0° apart. Star A is 15.0 ly from the Earth, and star B. appearing to the right of star A. is 25.0 ly from the Earth. To an inhabitant of a planet orbiting star A. what is the angle in the sky between star B and our Sun?

Chapter 1, Problem 1.73AP, You stand in a flat meadow and observe two cows (Fig. P1.73). Cow A is due north of you and 15.0 m

Figure P1.73 Your view of two cows in a meadow. Cow A U due north of you. You must rotate your eyes through an angle of 20.0° to look from cow A to cow B.

(a)

Expert Solution
Check Mark
To determine

The distance between cow A and the cow B .

Answer to Problem 1.73AP

The distance between cow A and the cow B is 12.1m .

Explanation of Solution

Given data: The Cow B is 25.0m apart from the observer. It is at an angle of 20.0° from the observer point to the right of cow A . The distance of the cow A from the observer is 15m .

Consider the following figure.

Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics), Chapter 1, Problem 1.73AP , additional homework tip  1

Figure (1)

The expression for the distance between cow A and the cow B is,

AB=OA2+OB22(OA)(OB)cosθ

Substitute 15.0m for OA , 25.0m for OB and 20° for θ in the above expression.

AB=(15.0m)2+(25.0m)22(15.0m)(25.0m)cos20°=12.05m12.1m

Conclusion:

Therefore the distance between cow A and the cow B is 12.1m .

(b)

Expert Solution
Check Mark
To determine

The angle between observer and the cow B.

Answer to Problem 1.73AP

The angle between observer and the cow B is 135° .

Explanation of Solution

Given data: The Cow B is 25.0m apart from the observer. It is at an angle of 20.0° from the observer point to the right of cow A . The distance of the cow A from the observer is 15m .

From figure (1),

In triangle OMA ,

cosθ=OMOA

Substitute 15m for OA and 20° for θ in above expression.

cos20°=OM15mOM=15cos20°m

Thus the value of the OM is 15cos20°m .

In triangle AMB ,

β=sin1((OBOM)AB)

Substitute 15cos20°m for OM , 25m for OB , 15m for OA in above expression.

β=sin1((25m15cos20°m)12.05m)=64.8°

The value of the β is 64.8° .

In triangle AMO ,

α=180(90+θ)

Substitute 20° for θ in above expression.

α=180(90+20°)=70°

Thus the value of the α is 70° .

The expression for the angle between observer and the cow A is,

θA=α+β

Substitute 70° for α and 64.8° for β in above expression.

θA=70°+64.8°=134.8°135°

Conclusion:

Therefore the angle between observer and the cow B is 135° .

(c)

Expert Solution
Check Mark
To determine

The angle between the observer and cow B .

Answer to Problem 1.73AP

The angle between the observer and cow B is 25.2° .

Explanation of Solution

Given data: The Cow B is 25.0m apart from the observer. It is at an angle of 20.0° from the observer point to the right of cow A . The distance of the cow A from the observer is 15m .

The expression for the angle between the observer and cow B is,

θB=180(90+β)

Substitute 64.8° for β in above expression.

θB=180°(90°+64.8°)=25.2°

Conclusion:

Therefore the angle between the observer and cow B is 25.2° .

(d)

Expert Solution
Check Mark
To determine

The angle between the star B and the sun.

Answer to Problem 1.73AP

The angle between the star B and the sun is 135° .

Explanation of Solution

Given data: The star B is 25.0ly apart from the observer. The angle of 20.0° between the stars from the sky and the distance of the star A from the earth is 15ly .

Consider the following figure.

Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics), Chapter 1, Problem 1.73AP , additional homework tip  2

Figure (2)

The expression for the distance between star A and the star B is,

AB=OA2+OB22(OA)(OB)cosθ

Substitute 15.0ly for OA , 25.0ly for OB and 20° for θ in the above expression.

AB=(15.0ly)2+(25.0ly)22(15.0ly)(25.0ly)cos20°=12.05ly

Thus the value of AB is 12.05ly .

In triangle OMA ,

cosθ=OMOA

Substitute 15ly for OA and 20° for θ in above expression.

cos20°=OM15lyOM=15cos20°ly

Thus the value of the OM is 15cos20°ly .

In triangle AMB ,

β=sin1((OBOM)AB)

Substitute 15cos20°ly for OM , 25ly for OB , 15ly for OA in above expression.

β=sin1((25ly15cos20°ly)12.05ly)=64.8°

The value of the β is 64.8° .

In triangle AMO ,

α=180(90+θ)

Substitute 20° for θ in above expression.

α=180(90+20°)=70°

Thus the value of the α is 70° .

The expression for the angle between earth and the star A is,

θA=α+β

Substitute 70° for α and 64.8° for β in above expression.

θA=70°+64.8°=134.8°135°

Conclusion:

Therefore, the angle between the star B and the sun is 135° .

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Chapter 1 Solutions

Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)

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