SOLUTION: A certain hill is represented by a hemisphere of radium 1km. A man 180cm tall walks down the hill from the summit S at 6km/h. How long (correct to the nearest second) will it be be

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Question 1141230: A certain hill is represented by a hemisphere of radium 1km. A man 180cm tall walks down the hill from the summit S at 6km/h. How long (correct to the nearest second) will it be before he is invisible to a person lying on the ground at S
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Answer by Alan3354(69443) About Me  (Show Source):
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A certain hill is represented by a hemisphere of radium 1km.
A man 180cm tall walks down the hill from the summit S at 6km/h. How long (correct to the nearest second) will it be before he is invisible to a person lying on the ground at S
:
S is at the summit of the hill which is the very top of the hemisphere
Draw a horizontal line thru the this point
Change 1 km to 1000 meters
Change 180 cm to 1.8 meters
:
the man's highest point is 1.8 + 1000 = 1001.8 meters from the center
A right triangle is formed point C to the center A, and a point on the horizontal line that is 1001.8 meters from the center (the man highest point)
find the angle at the center using the cosine
cos(A) = 1000%2F1001.8
A = 3.435 degrees
Find the portion of the circumference that the man walks on the hemisphere.
3.435%2F180 * pi%2A1000 ~ 60 meters
Find the time it takes to walk this distance at 6 km/hr in seconds
6000%2F3600 * 60 = 100 seconds