EBK LOOSE-LEAF VERSION OF UNIVERSE
EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 1, Problem 16Q

(a)

To determine

The distance at which a person will have to hold a European 2-euro coin to subtend an angle of 1°.

(a)

Expert Solution
Check Mark

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 1°.

Formula used:

The small-angle formula is written as,

D=αd206,265

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 1° can be calculated by using the small-angle formula, that is,

D=αd206,265

Rearrange for d,

d=206265Dα

Since 1° is equal to 3600, substitute 2.6 cm for D and 3600 for α,

d=206265(2.6 cm)3600=5362893600''=148.97 cm(1 m100 cm)=1.49 m

Conclusion:

Hence, the coin should be held at 1.49 m if the angle to be subtended is 1°.

(b)

To determine

The distance at which a person will have to hold a European 2-euro coin to subtend an angle of 1 arcmin.

(b)

Expert Solution
Check Mark

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 1(arcminute).

Formula used:

The small-angle formula is written as,

D=αd206,265

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 1 can be calculated by using the small-angle formula, that is,

D=αd206,265

Rearrange for d,

d=206265Dα

Since 1 is equal to 60, substitute 2.6 cm for D and 60 for α,

d=206265(2.6 cm)60=53628960=8938.15 cm(1 m100 cm)=89.4 m

Conclusion:

Hence, the coin should be held at 89.4 m in order to subtend an angle of 1.

(c)

To determine

The distance at which a person will have to hold a European 2-euro coin to subtend an angle of 1 arcsec.

(c)

Expert Solution
Check Mark

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 1.

Formula used:

The small-angle formula is written as,

D=αd206,265

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 1 can be calculated by using the small-angle formula, that is,

D=αd206,265

Rearrange for d,

d=206265Dα

Substitute 2.6 cm for D and 1 for α,

d=206265(2.6 cm)1=5362891''=536289cm(1 m100 cm)=5362.9 m

Conclusion:

Hence, the coin should be held at 5362.9 m in order to subtend an angle of 1.

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