Concept explainers
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?
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)
The distance between cow
Answer to Problem 1.73AP
The distance between cow
Explanation of Solution
Given data: The Cow
Consider the following figure.
Figure (1)
The expression for the distance between cow
Substitute
Conclusion:
Therefore the distance between cow
(b)
The angle between observer and the cow B.
Answer to Problem 1.73AP
The angle between observer and the cow B is
Explanation of Solution
Given data: The Cow
From figure (1),
In triangle
Substitute
Thus the value of the
In triangle
Substitute
The value of the
In triangle
Substitute
Thus the value of the
The expression for the angle between observer and the cow
Substitute
Conclusion:
Therefore the angle between observer and the cow B is
(c)
The angle between the observer and cow
Answer to Problem 1.73AP
The angle between the observer and cow
Explanation of Solution
Given data: The Cow
The expression for the angle between the observer and cow
Substitute
Conclusion:
Therefore the angle between the observer and cow
(d)
The angle between the star
Answer to Problem 1.73AP
The angle between the star
Explanation of Solution
Given data: The star
Consider the following figure.
Figure (2)
The expression for the distance between star
Substitute
Thus the value of
In triangle
Substitute
Thus the value of the
In triangle
Substitute
The value of the
In triangle
Substitute
Thus the value of the
The expression for the angle between earth and the star
Substitute
Conclusion:
Therefore, the angle between the star
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