2. A spacecraft is in a circular orbit about the moon, 1.22 x 103 m above its su
ID: 2039997 • Letter: 2
Question
2. A spacecraft is in a circular orbit about the moon, 1.22 x 103 m above its surface The speed of the spacecraft is 1620 m/s, and the radius of the moon is 1.74 x 106 m. If the moon were a smooth, reflective sphere , (a) how far below the moon's surface would the image of the spacecraft appear, (b) what would be the apparent speed of the spacecraft's image? (Hint: both the space craft and its image have the same angular speed) Answer: (1.07 x 105 m (b) 1420 m/s 3. An object is placed in front of a convex mirror, and the size of the image is one- forth that of the object. What is the ratio do/f of the object distance to the focal length of the mirror? Answer: -3Explanation / Answer
object distance do = 1.22*10^5 m
radius of curvature R = -1.74*10^5 m
image distance = di
1/do + 1/di = 2/R
1/(1.22*10^5) + 1/di = -2/(1.74*10^6)
image distance di = 1.07*10^5 m
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(b)
wo = wi
vo/do = vi/di
1620/(1.22*10^5) = vi/(1.07*10^5)
image speed vi = 1420 m/s
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3)
size of image hi = ho/4
magnification m = do/di = hi/ho = 1/4
image distance di = do/4
from lens equation
1/do + 1/di = 1/f
1/do + 1/(do/4) = -1/f
3/do = -1/f
do/f = -3 <<<------------ANSWER
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