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

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
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Where is S?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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) =
A = 3.435 degrees
Find the portion of the circumference that the man walks on the hemisphere.
* ~ 60 meters
Find the time it takes to walk this distance at 6 km/hr in seconds
* 60 = 100 seconds

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