(a)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(a)
Answer to Problem 16Q
Solution:
1.49 m
Explanation of Solution
Given data:
A European 2-euro coin has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Since
Conclusion:
Hence, the coin should be held at 1.49 m if the angle to be subtended is
(b)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(b)
Answer to Problem 16Q
Solution:
89.3815 m
Explanation of Solution
Given data:
A European 2-euro coin has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Since
Conclusion:
Hence, the coin should be held at 89.4 m in order to subtend an angle of
(c)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(c)
Answer to Problem 16Q
Solution:
5362.9 m
Explanation of Solution
Given data:
A European 2-euro coin that has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Substitute 2.6 cm for D and
Conclusion:
Hence, the coin should be held at 5362.9 m in order to subtend an angle of
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Chapter 1 Solutions
Universe
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