The moon is 3.85 × 10 8 m from the earth and has adiameter of 3.48 × 10 6 m. You

Question

The moon is 3.85 × 108 m from the earth and has adiameter of 3.48 × 106 m. You have a pea (diameter= 0.50 cm) and a dime (diameter = 1.8 cm). Close one eye and holdeach object at arm's length (71 cm) between your open eye and themoon. Which objects, if any, completely cover your view of themoon? Assume that the moon and both objects are sufficiently farfrom your eye that the given diameters are equal to arc lengthswhen calculating angles. Dime Pea    Both Neither Dime Pea    Both Neither Dime Pea    Both Neither

Explanation / Answer

The equation you use is =Arc length / Radius The of the moon is found by taking the ArcLength (in this case it is the diameter of the moon which=3.48x106m) and dividing it by the Radius (the distanceaway from earth which = 3.85x108m). So you have... =(3.48x106m) /(3.85x108m)=> moon=0.009038961rad Next you find the of the pea by taking its Arc Length (thevalue for the diameter, which = 0.50cm) and divide it by theradius (for this you use the length of the arm which hold the peathat = 71cm). You then get... =(0.50cm) / (71cm) => pea=0.0070422535rad Next you find the of the dime by taking its Arc Length (thevalue for the diameter, which = 1.80cm) and divide it by theradius (for this you use the length of the arm which hold the peathat = 71cm). You then get... =(1.80cm) / (71cm) => dime=0.0253521127rad pea

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